I don’t know the design of your bed so I don’t know what would be “normal” for that design but a latex mattress will do best on a firm, flat, non flexing support surface with slats that are no more than about 3" apart and good center support to the floor to prevent any sagging in the middle.
A very tight fitting cover is normal for component latex mattresses to help the mattress keep its shape and hold the layers together.
Handling latex can be somewhat tricky because it’s so elastic and “floppy” and can be bunched inside the cover and will also tend to “stick” to the layer below it. The trick is to lift the layers and wave or flick them into position and avoid pulling or tugging which can rip the latex and can leave it sitting unevenly in the cover. There are some videos in post #12 here that may be helpful and once you get the hang of it it’s much easier.