Strictly speaking, passage tickets should have been demanded at the entrance port. However....
Most first class passengers would come aboard with visitors. Furthermore they wished urgently to re-join their baggage which would go straight to the stateroom via a chain of stewards leading back to either the boat train or where the shoreside baggage gang left off.
The general effect was confusion. However, these passengers and their visitors, especially in 'colonial' ports where everbody knew just about everbody else, were not of that class which feels a need to stow away.
In these situations passage tickets would be collected by the bedroom stewards and rendered to the purser's bureau to be checked against the official passenger manifest.
It used to be the case that embarkation could not always be confirmed before departure. Nowadays, I would surmise that SOLAS regulations require this to be done.