Different prices at different times?

There is no surge pricing on Rover nor does Rover have anything to do with the fees charged by sitters. So merely viewing a profile doesn't trigger anything.

If you'd like to discuss with Rover Customer Support, their number is [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team].

I have seen the same thing and wondered why as well.

Most likely,the sitters whose profiles you viewed decided to increase their rates. This can be quickly changed at anytime. It’s possible that the sitters knew each other personally/professionally and discussed their planned rate changes, but it could also be explained by sitters’ awareness of the local market and considering their needs/value.