You're correct on how it works. That clamp is squeezed open in the station and it let's go of the cable.
In this photo, you can see 2 wheels on the left, and 1 on the far right. When entering the station, these roll in a track that supports the car. The high wheel near the center is pushed down by the track, compressing those springs, the ones that look like car suspension coil springs. That opens the clamp and releases the cable. Above the left wheels is a skid. There are tires in the station that push on this skid to move the car along the track, decelerating on the way in, slowly through the middle, then accelerating on the exit. The exit should have some downward slope so gravity helps the acceleration and lands the clamp on top of the cable. Springs are released and it's gripping the cable again.
Think of the track more like a slot that contains these parts through the station. Every detachable lift in operation, not just gondolas, uses something similar and have been around a long time. In your car, those same type of springs, probably 1 at each tire, support the entire weight of your car, a not trivial amount of weight (unless you drive a smart car).
That's a lot of force gripping the cable, it'll be fine.
The promotional videos show this.
Unless there's freezing rain. That freezing rain allows it to slip sideways in the track, in a direction it's not supposed to move in. Not a problem getting back on the wire, the ice is gone by then. But, it messes up the deceleration part of the trip when you disconnect. Snow is fine, and so is rain. Only freezing rain is the issue. A frequent problem in FL.