If you're playing in a local band, memorizing everything might be an option. My experience in bands was that the volume of music precluded memorization. If your show is 15-20 minutes, sure, but an hour of music is a lot, especially on keyboards.
Playing from music on mallets in an ensemble is harder than any other instrument I've tried. This is because the music can either be in the same visual space as the conductor or the keyboard, but it's not usually possible to see all three at once. This means that you either have to ignore the conductor or be able to play without watching the keyboard.
Since conductors don't like to be ignored, it's important work on playing music by "touch", glancing down to orient yourself, but focusing on the score. I sometimes play on a thin quilt over the instrument, which has the added benefit of making the sound softer for practice. Rely on your ear to correct you when you hit a wrong note, and get used to how different intervals feel, especially if you're doing 4-mallet work. Keep the sections small (like 8 measures, or even shorter depending on music density) at first, then stitch them together.
I agree with the commenter that it's very important to practice on something the same size/scale as your performance instrument. It sounds like the method your teacher recommended will work well in general. The only change I'd suggest is to keep looking at the music for cues. There's no need to memorize, you'll actually play better if you know the music well but can focus on interpretation and blend with other voices rather than just trying to remember what comes next.
Memorizing whole pieces in ensembles is generally a bad idea unless there is a large amount of time to rehearse or a number of people on each part (like in a marching band). It's very easy to "know you're right" and end up ahead or behind everyone else due to a memory blip. At the same time, memorizing hard spots, like page turns and tricky technical areas, is necessary. So you'll need to find the balance that works for you. Beginners will need to memorize everything, but as you become more advanced, you should memorize less and less. Soloistic stuff will need to be memorized, but you'll probably find you'll know the whole work on a deeper level by keeping the score in front of you and listening to the parts around you.