Should Invisalign trays fully cover each tooth? (Photo)

It looks like your dentist prescribed the use of power ridges, these are specially placed divots in the plastic aligner to add controlled force closer to the gum line.  These areas will always have plastic that is shorter than the teeth and may project the plastic off the tooth so that they do not feel smooth with the tooth structure.   In general, depending no the gum health and tooth situation plastic may be shorter than the teeth, just up to the gum line and in some instances extend onto the gum tissue.

It is hard to see from the photos you submitted, but it seems that the trays are properly covering your teeth