I have a professor that has given me some early advice on developing my thesis topic, but I have not yet formally selected a thesis advisor. I was thinking about choosing to work with a different professor whose research seems slightly more aligned with the project, but I'm curious if my professor (the one I already spoke with) will expect me to work with him, and if this would have entailed some sort of financial compensation for him. Not that this would heavily influence my decision, but it's something I'd like to be aware of.
I think such arrangements are uncommon. I've never come across them personally, though suspect that they do exist.
On the other hand, it is normal for such things to be "counted" as part of the teaching required, so that with "enough" such students the professor might be able to teach less in the classroom. So, some institutions have a rule that for a certain number of thesis advisees you will get a one course reduction in the load.
But in most cases, even if there is some financial incentive it would probably be pretty small. Where would the money come from.
But advising, both formally and informally is just part of the job. And most are willing to spend some time doing it informally as you have seen in your case. I doubt that there is any expectation that you will pick him as your advisor.
I have never heard of a professor being personally financially compensated for supervising a master's student. I'm not saying it never happens, but it would be uncommon, certainly in my country (UK).
However, while a professor is not financially compensated, they may be given funds to cover the costs of research materials - this money would not go to them, but to their lab's research budget. In some cases this can be a not inconsiderable amount of money (master's projects I've supervised have attracted budgets between £1000 and £3000). This money can be important because it is soft-money. That is, it can be spent as the supervisor sees fit (within normal rules of acceptable business use). For many of us, this is the only source of non earmarked money we have. So while our government grants might pay for chemicals and plasticware and reagents etc, this soft money might be useful to pay to repair computers, or send someone on a training course, or buy software subscriptions, etc.
Not typically, but it can be the case in some places. While in some countries/universities the salary is completely fixed, it is not fixed at all such places. At some places (countries or institutions), the salary depends on the financial situation of the department and this fluid part is distributed by the head of the department, hopefully by some objective criteria. Those would most likely be the productivity based on grants won, publications and teaching (including supervising some theses), because the departments receive their money exactly according to these criteria.
Additionally, the university or the faculty may have some fixed amount of money paid to the adviser of a successfully defended doctoral theses. Like this regulation by the rector of the Charles University (in Czech, sorry). The bonus depends on the number of years the student needed to complete the PhD and the maximum amount is 50 000 CZK (it is roughly 2000 EUR). For master's theses, one would only pay external advisors (not employed by the faculty) and only very little (say 1000 CZK). But the internal fluid part of the salary may depend on the teaching productivity, as I already stated.
In Czech Republic the master/bachelor theses advisors are professors, usually from the parent faculty, or some specialists from the industry.
The professors are paid for the advising the students - it is one of their duties in their contracts.
The specialists from industry have their ow contracts with the university directly or indirectly through their employer.
In respect to the student - (possible) advisor relation, the advisory is for free (the university through its funding is paying for the students). It's because they are paid for teaching you some skill (how to conduct a research, write thesis, defend your results). Being contracted by you it will be slightly changed to getting you the title.