Typically, funders require acknowledgement in every article that was supported by their funding.
So, what's actually getting supported by the funding?
- If you're a professor or researcher with multiple sources of support, then you are generally expected to account your time to each supporting project separately. So if you're supported 10% by a project, you only put 10% of your hours on that project, and only the things you actually do with that time get acknowledgement---i.e., publications related to the specific project.
- If you're a graduate student or postdoc, however, you'll often have only one source of funding that supports both your work on the project and your continuing professional development in general. In that case, you put the acknowledgement on everything, because it's all being supported by the same funding, whether or not it has anything to do with the original proposal.
Note that what's really important here is the accounting, not the position or the proposal. If funding supports you in create a publication, that funding must be credited, whether or not it's within the expected scope of the project.