Melody, I’m a bit concerned that you’re dealing with a CU rep who lacks even the most basic knowledge that should be required of anyone handling this type of transaction. You should be okay, though, if you confirm the following:
First (as Alan pointed out), the checks were issued payable to your credit union for the benefit of your IRA. That’s important so you have a direct rollover that isn’t subject to withholding. Based on your most recent message, it sounds like that is what happened but this should be confirmed.
Second, the checks need to be deposited in an IRA, not an HSA.
This type of rollover is not subject to the rule limiting you to one rollover per year. The reason has nothing to do with having an account sponsored by a health organization. You are moving money from an employer plan to an IRA, and that type of transaction doesn’t count as a rollover for purposes of the one-rollover-per-year limit.