It sounds like the change from glasses to contact lenses has caused a decompensating exophoria. It is important to check eye alignment before fitting a person with myopia with contact lenses when they have been wearing single-vision spectacles.
When people with myopia look through a negative spectacle lens at near, base-in prism is induced, and the person needs to exert less convergence in spectacles. Moderate levels of myopia are required for the base-in prism effect to be significant. Using Prentice’s rule (prism=decentration [mm] x lens power) with an inward eye movement of 2mm in each eye for near vision, a person with-5 DS myopia to obtain 1Δ base in. If a child you plan to fit with myopia management contact lenses has a large exophoria, that shows a slow rate of recovery on a cover test, an exo-slip on fixation disparity, and/or a reduced positive fusional range, then changing to contact lenses is very likely to cause decompensated exophoria. It would be beneficial to deal with the binocular vision issue first through orthoptic exercises to improve convergence and positive fusional reserves, before changing from spectacles to contact lenses.
The key to this is to carry out a cover test at near with the person wearing spectacles looking out for a slow recovery rate on an exophoria.