Squeeze is not the best term here. Tightness can cause serious problems, and will be confusing when the cellist attempts his/her first shift. Fingers themselves should build up strength. After the thumb is in place and you are accustomed to having it NEAR the second finger (there is a growing school of thought that the thumb should be near the first finger) I encourage and assign excercises to my students where they do not use the thumb at all on the neck.
Here's why: Prepare for a shift. What EXACTLY does the thumb do? It better loosen it's "grip" (ick) on the neck or the shift goes nowhere, or the thumb get's left behind. Let's talk philosophy on shifting. Shifting should come from the forearm, and nowhere else. Why? It's movement is along an x-axis and it should move along the x-axis line which is the fingerboard. This includes half-step shifts. Long shifts, such as octave shifting will have the torso move with the arm to help the arm's extension. Practice your octave shifts without the use of the thumb. Move the entire arm for the shift, let your torso follow the shift. You'll find your accuracy improves quickly. Now put the thumb back on the neck and use it as a guide to get to the heel of the instrument before the arm raises over the upper bout to approach the top note. Thumb ALWAYS moves with the shift and should keep in the same position in relation to the first or second fingers.
General rule of thumb (

) is to be able to draw a straight line from the second knuckle to the elbow without the wrist having any angle whatsoever, either bent or inverted. You'll find that your shifting, vibrato, and facilitation of finding notes increases exponentially, instead of working hard on it day in and day out.
Finger strength is very important for so many reasons, hence the need to become independent of the thumb. Vibrato usually has little or NO pressure of the thumb. Shifting requires little or NO pressure of the thumb. Thumb is just a guide, no more. I would encourage all cellists beginner to advanced to play baroque music with the thumb nowhere near the neck to discover this for themselves.
When playing above 4th position, remember to keep the straight line between elbow and knuckle. Getting into this habit will prevent you from getting stuck on the corner of the upper bout.
I'll post some pictures on this at some point.
Paul