Okay! This kind of fashion/gear I know!
Workout tanks like the one pictured, usually have a snug fitting internal bra-like part sewn in at the straps, but separate at the bust (fitting over and under the bust, and holding the girls snugly in place) while the tank then is a second layer that meets the top of your bottoms.
Some tanks have the bra part be more a part of the tank, like a sports bra with a longer part under the bust that goes to the top of your bottoms.
If the tank does not come with a build in bra, it is usually considered a 'singlet' and hangs loosely from the body, providing coverage, but no support. You will need a sports bra with this type of garment.
If it is a nice soft tank that clings to your body without any support, or a loose fitting shelf bra...it is then not real workout gear, but rather sporty fashion. You want a snug fit in your gear, to keep the girls in place and prevent friction on sensitive parts.
If you are working out, expect to sweat, and embrace it. Good 'ole sweat marks on your back, around your neck, and arm pits, and under your bust. Get out of your gear as soon as you are done. DO NOT get into the habit of lounging around in it!
Showing a little nip is par for the course with these type of close fitting high Lycra items. If it bothers you, go for a busy print vs a solid colour.