If you passed the "real" psychometric tests (the online ones don't count, they're just used for screening) at another company, if it was within 5 years your results may well be good enough that you don't need to do them again for CrossCountry - if not then you'll have to do them again. I'm in the same situation, recently passed paper, computer and MMI with Transport for Wales - but they only do the "national" standard tests so I'm pretty sure I'd have to redo all the tests for CrossCountry if it gets to that point.
There is also the two lives restriction, that means if we fail the assessments twice (or is it just they can only be taken twice overall, regardless of result - someone correct me if I'm wrong) then we can't take them again.