They make and take the card someplace that runs the cards manually...you know, with the old-school validator like this:
The bank has no way to know when it was done, only when it was submitted; they're dated but the date can be easily forged. (Often the crooks have the damned thing, you can buy them on eBay...I wish we'd auto-contest every manually-validated CC ticket (nobody legitimately uses them anymore...we had one in the branch because we legally had to be able to process card-withdrawals in the case of natural disaster, power outage or system-offline. Most non-bank places just put up a "no debit or credit" sign in that scenario) but Visa/MC says that's too merchant unfriendly.) So, SOP is to assume all receipts dated before the card-loss as valid until contested.
Or they use whatever ID-faking they can (meaning they use the information I asked you if they asked for, to obtain legitimate IDs...because the best fake ID is a real one obtained illegally.) they go into a branch (and look for the newest, nervousish, gullible teller they can find) with a sob-story about someone f**king with them ("My separated-husband reported my cards stolen because I filed for divorce" being a popular one) and the teller, after looking at it in the system, asks for ID and rather than doing what they're supposed to do (refer to branch management) they force-approve the transaction because the ID is real and valid and they think they're doing the right thing.
On your card, you've done as much as you can. The bank is responsible now for any subsequent issues. Just watch the statements for the next few months for anything unusual. Also, you're entitled 1 free yearly copy of your credit report. Wait 60+ days and have that run (you want to run it as soon as possible but after they're likely to have used the information...you don't want to run it tomorrow and find out a year from now they opened a no-limit Visa Black card on your immaculate credit one day after you ran the report and bought a jet. You're not responsible but it'll be a pain to fix and screw you up for months while it's being fixed.)...the bank can do it or there are websites maintained by the three major credit bureaus that can do it. (Information here*) Don't use the ones you see advertised on TV...they're for-profit companies. They'll give you what you're entitled to but they often use small print to get you to agree to subscription or credit-monitoring services (up to $24.99/month!). Your report will show you if they've managed to compromise your ID and use that information to open accounts or cards with your information.
As for how they access the other cards on the account...that's a bit tougher...usually doing that requires a lot more effort than they're going to put in and it's high-risk for them. (When they get caught, it's being this dumb.) Just watch his card too for suspicious activity.
*-
http://www.ftc.gov/bcp/edu/pubs/consumer/credit/cre34.shtm