It's current phase of gradual decrease with great peaks will stop at about 13th July. From there, we will either see a long, stagnant phase like 2013BTC (if I've gotten the year right it's that or 2012 although I think I've got it right) where it rises dramatically, has a double peak and then decreases gradually, although this time looks a bit different due to the third peak and the different peak heights (there are similarities and differences, got the comparison from The Contrarian Dude).
The difference in dates for the RSI and price fib time zones is probably going to be the RSI changing phase and adjusting itself for reflecting in price changes.
I believe it's very likely we get a great price increase as the next price phase - perhaps it starts increasing greatly along the price fib which reaches 110, although I have no idea how to judge which level it will go to yet.
The price decrease fibs I've drawn where the price goes down to the blue level indicates that we're probably actually at the lowest point now. If so, we'll see a significant price increase until 20th June; when the RSI cycle changes. I believe that this will present itself as a transition phase - the peaks/troughs probably forming a curve of some sort with either the RSI or price.