This is why I love ELL! I would have never thought about how such a natural-sounding phrase could be so confusing. But considering how the word catch has well over a dozen meanings (just as a verb), I can understand how this might be hard to catch. After all, we can catch a ball, catch a bus, and we can catch a thief. We can also catch a disease, catch someone's drift, or catch someone's eye – so how can we possibly catch our son over the telephone?
Collins lists 20 meanings of the verb catch, and not one of them fits well with this context. I think the closest might be:
catch (v.) to overtake or reach in time to board ⇒ "if we hurry we should catch the next bus."
Obviously, the caller won't be boarding her son, but the concept is similar: If I'm too late to the bus station, I won't be able to catch the bus. And if I call your house too late, I won't be able to “catch” you before you depart, either.
Macmillan lists a meaning that's more of a direct hit:
catch (v.) to find someone available to talk by going to or telephoning them at the place where they are ⇒ "Call me at the office. You can usually catch me there after 8:30".
As the other answerer mentioned, it's not an unusual use of the word at all. It's commonly used this way both at home and in the office.