Ok, it's pretty much what I expected.
Osmosis is, in a nutshell, the movement of water down a concentration gradient. A membrane, permeable to water and some other compounds, divides one volume of water from the other. The water from the side with the least amount of dissolved particles will tend to move towards the side where the water has more dissolved compounds. Only compounds that cannot cross the membrane are considered. If they can cross the membrane, they do not affect osmosis.
The extent to which water from what side will tend towards the other can be counted as the osmotic pressure. This is the force that is required to stop the flow.
A RO unit will take your water and apply enough force to cancel then reverse the direction the water would tend to flow, so, much more pressure than the system's osmotic pressure.
My guess for the increase in your pH is that the membrane is permeable to CO2, but not to carbonate or bicarbonate. So dissolved CO2 will pass, but the other side will become more and more enriched in carbonate species. CO2 and carbonates are related as follows:
CO2 in water forms a little carbonic acid:
CO2 + H2O = H2CO3
Dissociations:
H2CO3 = H+ + HCO3-
HCO3- = H+ + CO3--
As the RO process goes forward, as mentioned above, the carbonate and bicarbonate will be concentrated on one side. The equilibriums will shift to the left hand side.
This process will consume H+ (raising pH) and produce CO2 which can move across the membrane.
At the end of the process, you should have produced water with a higher pH and a higher CO2 content. However, given a bit of time, the RO water will reach a new equilibrium with both the atmosphere (since your tap probably wasn't to start with) and the increased CO2 produced in the RO process.
In short, give it time, and it will come down.
Oooof.
