I would second that I never experienced "aggression" with starting testosterone. I noticed emotional and mental changes just about right away (though, no doubt, some of that was simply euphoria from actually starting the medical part of my journey).
While I never experienced aggression at all, there were plenty of times I felt more easily frustrated than I had before because my emotional landscape felt different than before and I had to relearn how emotion came to me and how I could purge the well, so to speak. I lost the ability to cry easily pretty quickly. This was a huge relief to me because, even when I didn't present male, I cried all the time for any strong emotion. Unfortunately, that also left me bottled up with no physical way to relieve strong emotion. For me, both before and since starting T, strong emotion always comes with a need for physical release. I found ways to relieve that in working out or running and found as long as I did something physical routinely, the peaks were not as sharp emotionally.
I tend to be an introspective person and have always enjoyed analyzing myself (for good and bad). So I spent a lot of time in the first 4 months or so trying to figure out what exactly I was feeling (sadness, frustration, embarrassment, anger, etc) and what the trigger was for that feeling. That helped me build a new map of my emotional landscape. That certainly helped my frustration with not really understanding the new way emotions came to me.
I know there are plenty of people that say testosterone "causes" aggression and it certainly may make it easier for people already prone to anger or aggression to express that outwardly. But, for me, I never experienced aggression or increased anger/rage/etc. I'm genetically laid back, though. My parents are not quick to rage and that wasn't the way I was brought up, so that might just be me at my core anyhow. I do know I am happier and more confident. I'm about a week and a half shy of 5.5 years on testosterone and it just continues to get better to be able to live as my authentic self.