Chamois Supposed to be Tight in Crotch?

We're all adults here.

When wearing well-fitting bib shorts, a male should feel "cupped" The legs of the bib shorts should touch the skin all the way up the thighs, through the "curve at the top of the leg to scrotum" and around the whole area.

Your old-fella should be pointing forward, slightly cupped by the cloth so it points up towards your belly button.

One way to get a good fit is to pull the shorts on, and wearing nothing more, lie on your back on a bed. Pull one knee up to your chin and leave the other leg more horizontal. This will help get the cloth up to the aforementioned curve. Swap legs and repeat. You should be able to do this without cloth sliding past your skin, and without any large air pockets/spaces being formed beside the legs/scrotum.

One possibility is the cuffs of your bibs may be too low down your leg/thighs. You should pull the legs upward to free material for the crotch area.

Also, if you stop for a toilet break, this will disrupt the lay. So do your best to reestablish the cloth up to the curved area.
The padding should be inside the shorts, not on the outside where its visible to the world.
Chamois cream can be helpful too, but I only wear it for long rides of over 100 km. This also goes on the skin, or sometimes on the padding.
Lastly, nothing else goes between padding and skin, so no underwear. The bottom of your T shirt or baselayer is fine to be in the area, but shouldn't be long enough to get that low into your bibs.

---

^{There's got to be a better name for "that curved bit between inner thigh and nutsack"}