Might be just me, or might be because English is not my native language, but the use of possessive to designate people who work with you (albeit in a position that feels like it's inferior on some org chart) always sounds patronizing to me. Does it really not in English ?
Not against you personally, I just could not keep this feeling within for longer.
/out-of-topic
I would interpret some one saying "my guys" in this context as a sign of respect. It can be roughly understood to mean "my go-to guy." It has the connotation of a well established, high-trust, working relationship.
For example, if I needed to get my car serviced and someone was trying to pitch me different mechanics I would say, "I got a guy" to indicate that I already feel looked after.
As others explained, it is common usage in American English.
The bigger problem to many contemporary readers may be the (I am sure unintentional) sexism in the phrase "my guys".
Instead of "Every one of my guys says", another way to say it would be "Everyone on my team says". Or maybe even better, "My teammates all say".
Of course we have to keep in mind that these are all just late night off-the-cuff comments, so some gaffes may be expected and accepted.
Edit to address the thoughtful replies below: I think whether "guys" is gender neutral or not depends on the context and culture. Informally and in personal conversation, sure, if the "guys" in question don't mind it. Here on HN, doesn't matter too much. In formal writing or business communication, it would be something to avoid.
I generally try and be mindful of stuff like that, and were there any women on my team I wouldn't have used guys. Unfortunately covid plus unrelated personal issues caused the only woman on my team to have to resign last year. I do sincerely hope I can get some women to apply this hiring round, because diversity is important to me.