This is a great question! And something I definitely worried about before starting hormones. I had heard so many first and second-hand accounts of people on T changing drastically, becoming really emotionally unstable, angry, violent, etc.
I have a couple theories about why these stories circulate, but take 'em with a grain of salt haha. Some of it is just transphobic (not to mention biologically essentialist) myths that are circulated around that testosterone turns everyone into big angry monsters. Some of that probably comes from what I usually call "butch puberty" (aka the phase some ppl go through when they're first figuring out how to "be masculine" or "be male" and they think that being angry, aggressive, or jerky is the best way to do that. A phase which sometimes coincides with starting T). And some of it honestly probably has a lot to do with timing and dosing.
(Going to try not to get too specific here, so as not to breach the TOS) It's pretty common for doctors to prescribe very high doses of hormones from the get-go and to encourage bi-monthly injections. That means you're putting a LOT of hormones in your bod at once, and you have a whole 2 WEEKS for them to sort of "cycle out". Since my mental health was terrible just before starting hormones, and I had PMDD (a very hormone-sensitive subset of my mental health issues), and I was terrified of the idea that T could change my personality, I decided to start on a very low dose (about 1/4-1/8 of a typical starting dose) and slowly work myself up over the course of a few months. I also decided to do an injection weekly instead of bi-monthly, so that my "cycle" would be shorter and more controlled. I had noticed a lot of people on T talking about the emotional changes they felt immediately after their shot, or for the few days before their shot. These descriptions often sounded like issues related to having too much or too little, or just not the right balance of hormones in their body. So it made sense to me to decrease the possibilities of those changes by injecting weekly.
I'll probably make a separate post about that and about how it impacted my singing voice, etc. but feel free to ask me any questions if you want me to elaborate on the topic here.
Long story short, this method worked wonderfully for me. It really helped with my mental health (which got exponentially better very soon after starting hormones). I'll always be someone who struggles with mental illness, but it helped with the ways that dysphoria was triggering my anxiety, and it essentially cured me of the PMDD which had been making me suicidal before my period pretty much every month for a decade. That method also let me sort of ease into the changes.
I personally never experienced any dramatic emotional changes except for the steadily increasing stability of my mental health. I'm still the same person and most of the changes in my personality in the last year and a half come from my experiences of being read as visibly trans and with the rock bottom I hit before starting t. I am definitely still able to cry, and have had some real devastating cries throughout this last year. But I do cry less often. Strangely, often when something would have made me cry in the past (like a sad video) now it gives me chills through my whole body. So I'm still having a visceral physical response... just a different one!
Anyway, that was long-winded but I have lots of thoughts on the topic so feel free to pick my brain. Best of luck to you!