Some tutors do, and some don't. Those who do have varied motives.
Some are screening to make sure that the child does stand some chance of passing, rather than the parents wasting their money or pushing the child to do something they are not capable of.
Others are screening because only taking the very brightest kids means they get an easy life and a good crop of pass rates to show the next set of parents.
Some are perhaps a combination of both. Only you can tell where this tutor falls on the scale.
The assessment should not be a full-blown 11+ paper, but is likely to be a Verbal Reasoning paper of some sort - one that is geared to the child's current age and lack of experience of VR.
I shall be most interested to hear the thoughts of others on this, especially Patricia & Mike.
It is interesting to note the difference between your two children - what works for one will not necessarily work for another. Mine are just the same!