Actually, "off-peak" here has nothing to do with cell phones or plans. She's talking about landline rates, possibly long-distance landline rates. It was very common even in the US circa 1999 for your landline phone to have multiple rates for both local and long-distance calling, but very much more so for long-distance. Cell phones were beginning to become common at this point, however they weren't really suitable for any sort of data transmission at this point in time beyond simple text messaging.
Source is me; I graduated from HS in 99, knew lots of folks who had to deal with this because their parents had cheap landline phone service.