If both of you desire it, then your Palien companions can travel outside with you, and that may be recommended for the larger variants who agree to carry you - whether that's riding along the routes, flying, or going across water.

[One must ride something, after all.]

However, for many, the Pokeballs are often preferable. It allows them some measure of privacy, and lets them rest in peace.

There are actually a variety of Pokeball types, some which seem better suited to particular Paliens... I suppose that means a part of their construction must be especially appealing to them in some way? At any rate, you need not worry. They seem to have no issues with whatever is inside.