This is interesting! I see that you are in London. Welcome!
First off, you need to fix your rate table. The puppy rate is not an add-on, but the actual amount Rover will charge any customer for house sitting a puppy. Since most people charge more for puppies, you need to fix the table for the actual amount. Since you charge £50 for house sitting an adult dog, your puppy rate needs to be entered as £75 if you intended there to be a £25 surcharge. This is probably why you were contacted because the customer only saw £25 for her puppy's daily care, which is way too low.
For your specific question, house sitting is supposed to be for 24 hours of pet care. However, you should be free to take care of other pets (walks and drop-ins) while on assignment at the other home. You are not physically tied 24/7 to that home. However, with a puppy, you are going to need to be there much more and be sure the puppy is crated or otherwise kept safe if you leave the home.
I hate to say that if you charge the customer £75 per night for puppy care, I would expect you to do all the feeding and walking you've described. Seems quite reasonable. If the customer is only seeing £25, then you need to fix it.