AP, Tiger's Fury, Mastery, and Combo Points are snapshotted when a DoT is cast. This means that If you put Rake up, and then your SuperAwesomeAgiTrinket procs, the existing Rake will not gain a benefit from it. In the case of Rip, when you refresh it with Ferocious Bite via Blood in the Water, it will resnapshot everything except for the number of Combo Points. This means that if you put a 5 point Rip up, and as long as you keep on using Ferocious Bite with any number of combo points, you will keep a 5 point Rip going. It is also a good idea to try to get the 5 point Bite off when Tiger's Fury is up.
When you cast a DoT when the same effect is already present on a mob, it will put a new DoT up that lasts for the base duration plus the amount of time till the previous effect would have ticked next, and the next tick will occur when it would have if you had not "refreshed" the Dot. For example, if you hit Rake when Rake has 2 seconds left, the new Rake will have a 17 second (2 + 15) duration and the next tick will occur in 2 seconds. This makes it ideal to refresh DoTs when there is less than one tick remaining (2 seconds in the case of Rip, 3 seconds in the case of Rake).
Keep in mind that Rip refresh still checks Combo Points and AP and will sometimes fail with "A more powerful spell is already in effect.". While this is annoying, this does not actually cost you much DPS as long as you are good about hitting Rip exactly when the old one drops off when this happens.