In my experience there are commonly three things that cause a bandsaw to cut incorrectly.
1. A blunt / poor quality blade. If you have problems first off buy a decent blade. I recommend Tuffsaws, Ian produces high quality blades that run true.
2. The tension on the blade is too low. Chances are, the bandsaw spring is inadequate or has been over compressed. Compressing a spring by more than circa 25% destroys them, and they need replacing. Bandsaws don’t normally have stops to prevent over compression. Also the tension guide on the saw is probably next to useless and won’t be calibrated to the blade you are using.
The majority of issues are covered by poor blades and blade tension.
Sideways wrote a thread on restoring a SCM bandsaw where we went though spring theory, selection and setup which is universal to just about every bandsaw.
https://www.ukworkshop.co.uk/threads/scm-minimax-s45-bandsaw-teardown-overhaul.135069/
3. Setup. There are a few that fall into the category, people get sucked into blade guides and what’s best. They do absolutely nothing for cutting straight. I know, controversial idea, but they are only a safety device not involved in anyway with cutting stuff. I write a thread on the theory. However they get the guides touching the blade which is simply wrong, which deflects the blade and causes it to heat up / follow an unnatural path.
https://www.ukworkshop.co.uk/threads/bandsaw-blade-guide-theory.135481/Blade alignment to the fence, mist have saws have a way of aligning the blade to the fence for straight cutting. Mist are not aligned and the user ‘fights’ the natural cutting path of the blade causing heat.
Blades coming off the wheels are usually blade tension, or alignment of the bottom wheel.