I would think the money would stay in the IRA, just not be invested in a CD. Kind of like how money that's not invested is still in an IRA. I could be wrong though, as I've never put money in an IRA CD.
Worst case, if it does somehow get booted out of the IRA then this will be a 60-day rollover (as long as it get's in to the Ally CD IRA within 60 days of when it's distributed from the Other bank's CD). You can do only one of these per rolling 12-month period (not calendar year), so be careful with that, but otherwise it shouldn't matter.
I would be concerned that the bank is saying something is different because he's over 59.5. The only difference about being over 59.5 is that you can make qualified withdrawals that aren't subject to an early withdrawal penalty, but you'll still pay tax if it's a traditional IRA, and you can't put the money back in an IRA except through a 60 day rollover. Given that comment it seems like someone isn't understanding something about this.