The Auror escort is because the location of that house is secret. Only a few people are allowed to visit without Sirius explicitly asking for them. This isn't standard practice, but lots of people on both sides might still be interested in getting revenge on Sirius, based on what they believe ze did or didn't do.
The Aurors weren't literally “your [Granger's] people” at the time, but the phrase still works. It's also possible that Harry is using “your people” to mean people in authority in general, as Granger has been on that track almost since the day ze arrived in the magical world.