Well they shouldn’t really pop out that easy. There needs to be a tight fit between outer and the cup. If they were loose you’d get all kinds of problems.
You can get rusting going on, though if they were fitted tight the rust will mainly be on the edges facing you. I only see rust with poor seals and excessive washing.
The proper way is to use a bearing extractor. The normal way is to hammer away from the other side with a flat bladded screwdriver / drift /etc 😉 , going carefully but forcefully around the bearing to walk it out. If the bearing is getting replaced, don’t worry about damaging the bearing.
New bearings in, use a smear of grease on the outer surface.
Assuming we’re talking cartridge bearings though.
Bearings – http://simplybearings.co.uk/