The probe should be used for the hot side and the actual thermometer should be placed near the cool side hide. I wouldn't put it right on top of the hide, but next to or in the general vicinity of it should be fine. I lean mine upright against the glass.

Yeah 90 is a little too hot for the cool side, but it is probably a couple degrees cooler inside the hide as opposed to where you had the thermometer. If it the temp continues to read 90 on the cool side even with moving the lamp around then I would maybe switch to a lower wattage bulb