"I don't like to ask my manager, "what to do", while he may sound nice or not. It all add up to my evaluation of my probation in the end."
The ticket system was put in place for a reason, which is to document requests for support before any work is actually performed.
You'd best run through with your manager what you must actually do when you receive email requests, especially those of an emergency nature.
If you take it upon yourself to work on undocumented requests and the outcome of the work you have performed is also undocumented, you would end up in hot water with the manager if the manager were me. If you don't know something, you ask - that's what your manager is here for. You don't guess and you don't ask on Stack Overflow because none of us here has an inkling how tightly your company is enforcing its ticket policy.
You are lowest on the totem pole, so it's incumbent on you to ask before you do something that your management would regard as ignorant, stupid or harmful. And doing stuff that's stupid, ignorant and harmful won't help you get past your probation period. Especially if you could have avoided doing something ignorant, stupid and harmful by the simple expedient of asking. Ignorance is a luxury you can't afford. As your manager, I'd distinctly prefer that you ask me something stupid than you doing something stupid on your own. I need to have the confidence that you'll ask me before you do something stupid. Your top priority at this point is "do no harm".
Every company I ever worked for and for which I performed client support - that company had a policy of strict compliance with its ticketing system if it had a ticketing system in place (*). Your employer is most likely no different and you simply need to discuss with your manager what to do with these email requests.
(*) The strictness makes sense since any ticket includes time stamp, description of the issue, history of what was done to resolve or manage the ticket including what was tried and didn't work and what troubleshooting took place, who was involved in resolving and managing the ticket, who currently owns the ticket, the priority and urgency that's currently assigned to the ticket and the current status of the ticket - whether it's open, closed, on hold, etc. I expect that none of the emails you get has most let alone all of that vitally needed information.