Asking about funding when you've already been told you'll be funded
It's common for funding to end during a prospective PhD student's expected stay, especially in places where a PhD takes 5 or more years. If grants are for about 3-5 years then this is almost a certainty. It's not unusual to get a student late in a funding cycle - maybe there wasn't an appropriate student for the role until now, maybe a prior candidate went someplace else or left early.
However, yes, it's a bit of a short window to have this funding already expiring within the next year. Sometimes there are other funding streams for a lab, sometimes there are possibilities for non-competitive extensions. You don't have enough information to know this is a problem.
All these uncertainties make it an uncomfortable but also necessary conversation to have. A PI should be comfortable talking about funding plans and contingencies and you should definitely ask about it. PhD programs should also have information about what they do when there are funding issues. For example, is there some department funding that can help cover a student if there is a gap?
Definitely ask your professor about funding. Avoid being accusatory and alleging any sort of misrepresentation, and just go in with questions you have: how long is funding actually secured for? What are the plans when it runs out? What happens if those plans fail?