I have been applying to some universities for semesters starting in Jan 2024, and I expected that I can receive the decision letter in 2 or 3 months later.
However, 2 months ago, a professor actively emailed me (he knew me because another professor forwarded my Ph.D. inquiry to him) and he wanted me to come in the Fall semester for a project. His offer was really good and I wanted to keep his offer as a backup option, so I said that I'm interested in his offer and promised to send my applications in the future. However, I made the big mistake of not telling him that I was also waiting for other universities.
A week ago, he emailed me again to say that he had finalized the grant for me and was ready to recruit me immediately for the Fall semester (despite that I hadn't submitted the application to him) and wanted an answer from me. I had to admit that I couldn't accept his offer now because I also waited for other universities.
Now I feel extremely guilty and embarrassed because he probably had to do a lot of things to acquire his funding and now I just made him waste a lot of time and effort.
I just wondered if any professors get into this situation, how can they solve it?