tool I developed as my PhD dissertation.
What kind of tool? Over here (Germany) the copyright (i.e. the economic exploitation rights) for software are by default owned by the employer, i.e. possibly your university if you had an employment contract for your PhD work. If we're talking about a software tool, they need a license by the owner of the copyright.
Copyright wrt. the dissertation itself is not of importance here unless the company wants to make copies of the dissertation or quote/reuse parts of it (as opposed to using the methods described).
Methods and knowledge described in the thesis: unless there's a patent (which would grant the patentholder the exclusive right to use e.g. that method), everyone is free to use whatever they learn from reading your thesis. Just as you are free to use everything you learned from reading any other book or paper.
The company doesn't own my dissertation knowledge - or do they?
No, but they also don't need to own your dissertation knowledge in order to use it. (With the exception of their employees including you) they also cannot forbid anyone else to use that knowledge: they'd need to own a patent on that knowledge (or the copyright for software) to do that.
The important idea behind the patent is that the exclusive rights are granted in exchange for making the content of the patent public, i.e. from the point of view of patent law, you had the choice to keep it private (unpublished). But patent law requires you first to think: if you want a patent, i. e. to forbid others to make use of your knowledge, you need to declare that before making the knowledge public. If you don't want your knowledge to be public, keep it secret and neither ask a patent nor publish your knowledge. If you want to make the knowledge public, but don't want to forbid anyone to use it: fine, no need to file a patent, just publish it.
Which is what you did:
A normal PhD thesis is public (and published) in every sense of the terms, and so are your research papers.
I am worried that [...] they will continue using my science, continue not crediting me, and I will feel cheated, even though I brought up the idea of using it while working here.
No point in feeling cheated here, see above. If there's anything you could feel cheated about it's that you did not file a patent (in case that was possible: not all gains in knowledge can be patented or protected by copyright).
Any other company, including competitors of your current employer and any future employers of yours can use the knowledge they get from reading your thesis, just like your present employer.
Still, you may want to consider whether you like to work for an employer who turns out not be very generous (after all, saying thank you and that your contributions are valuable and publicly crediting you for your contribution costs more ego than money).
Lack of citation: The company is trying to represent the work as a "Company Project" and they have removed all citations and mentions of me individually.
Unless they try to get publicity by writing a scientific paper (where the usual academic standards for citing the source of ideas apply), they are bound by copyright. I.e. they need to cite (and possibly obtain a license) only if they quote or reuse tables or graphs from your thesis. Copyright btw. does not cover fact knowledge (if you measure and publish the density of pure water at 4 °C, others can use and quote your numbers without the need to obtain a license. Databases are different, though, and may not be reused without license)
I was told all press contact must go through our Marketing department, even though I have been contacted independently by journalists that saw me present this project / my science at conferences earlier this year. I am not supposed to speak with them, and instead redirect them to our Marketing group. I find this very odd.
(Side note: I found it even more odd, when I encountered a similar situation in an academic research institution)
IMHO it is within the rights of your employer to decide who the contact/spokesperson for the company project is. IANAL, but I don't expect* the company can forbid you to talk to journalists about your PhD thesis.
Whether you want to ruin your relationship with your employer about this question or whether it would be strategically a much smarter move to say that as you are interested in that project since long before they ever became aware of it, you'd like to be more deeply involved in this - and this way try be the important guy first marketing talks to about the project and after a while try to get a sufficiently public position.
The other recommendation I have is: try to find out why you are not supposed to speak to the journalists. A couple of reasons that for me would lead to totally different conclusions come to my mind:
- Your company may be working towards a patent right now. That hypothetical patent needs to achieve a certain non-negligible advance over the state of the art. Everything described in your thesis is already state of the art, so they can patent only new inventions on top of that. But they may be afraid that you accidentally reveal relevant internal information to the journalist - and that would make that revealed knowledge also state of the art and thus endanger the patent. The marketing guys may be pros in realizing what internal knowledge must be kept internal - wheras your employer may (rightly or wrongly) think that you are still more in academic mode and tend to tell things.
(I'd probably try to be involved in any such patenting project, but think this a sensible reason)
It may be the general policy that marketing/PR is the only point of contact of the public.
(Whether I'd think this a sensible reason or not would depend - but if the general PR policy of the company doesn't suit you, this should enter your thoughts about what you want for your professional future)
They may try to gag you and get out all your knowledge and then ditch you.
Of course, not sensible/acceptable.
* For Germany I have learned that broad gagging clauses in the employment contract that try to forbid more than what an employer can claim legitimate interest for are totally void. Together with the extremely employee-friendly court rulings we have here, I'd feel completely safe talking about my thesis work of 5 years before joining my current employer.
For the whole answer: keep in mind that I'm most used to Central European (German) legislation and working customs. Your legislation and work culture may have a different view on some of these aspects.