Yes, it can.
Mainly Pseudomonas bacteria in the air (against which benzyl alcohol has little effect). Staph that shed from your skin, body hair/hair. Possibly a few fungal spores from you and your clothes. Above all, the entire microbiome surrounding you within a radius of about one meter, which you release with every exhalation. Enough? ;-)
That’s why you need to thoroughly disinfect your hands or wear alcohol-treated gloves, remove watches and jewelry, wear a mask (I still have plenty from the COVID...), and work in a clean, windless environment (nowadays, I have to turn off the AC and fans, and with it being 40°C outside, that’s tough!).
Watch nursing training videos to learn best practices.
Definitely avoid random YouTube videos (especially PepCritic; I just watched one, and it made my skin crawl how badly he does it!).
I prepare the recons in batches in pen vials. The venting problems you have don't occur when injecting with a pen. It's really a consequence of the multi-dose in a vial.
I put a hairnet on my head and a non-woven lab coat during recons (not during injections). They're really inexpensive, and you can use them for a while: when you're working alone, there's no risk of cross-contamination. Just, watch out for the cat!
You can use a filter attached to the end of a vent needle to equalize the pressure. This filter can be reused for a while if you store it properly. PTFE is good for air, but PES is okay too. 0.1µm PTFE if you’re really paranoid ;-) Even paranoids can have enemies: Pseudomonas and Staphylococcus are nasty.