There is a problem. This is an illegal requirement. They can ask "pretty please," but this would still be sketchy.
Amazing what can be 'required'. If the employer doesn't enforce or penalize (discipline) then no violation. You have to prove harm (discipline) for your service for their to be a violation. Employers can demand all sorts of things, (orders under 30 days, etc) the assumption is you know your protections under USERRA. Don't comply if a violation, and if no discipline etc, then you have what our FOM says. Doesn't require you actually comply when contradicts USERRA.
Best to talk with your Mil reps, Capt Wright at ROA, the ESGR, etc to determine if one thinks a violation. Again, imo, DOL VETS assumes you know your protections. Just because you are asked, told, cajoled, required to violate USERRA, don't. If penalized, document and take forward. Contracts are similar. Don't know it at your own peril.