As we discussed in the current slaked lime thread, carbo distributes itself according to the pH. At pH 7.1 16.1% of it is H2CO3. With an alkalinity of 214 the total carbo is 5.276 mmol/L resulting in 48.6 mg/L H2CO3. That's more than the water can hold i.e. it is supersaturated with H2CO3 and carbon dioxide will leave the water over time (a couple of days) and the pH will rise until the water is no longer super saturated. It will probably finish up around 8.
Now that's just part of the story. pH meter electrodes are not exactly rapid response devices. When you move an electrode from one medium to another whatever it was in last adheres to the bulb and junction and needs to be rinsed away with sample. If you are doing things right the previous medium was a squirt of DI water and you should have blotted it away but that is still a different medium from the sample and the comment still applies. It definitely speeds things up to swish the electrode through the sample to accomplish this removal of the previous stuff but that alone doesn't insure quick response. It takes time for the glass of the pH bulb and the reference junction to come to equilibrium with the solution. Over time the bulb, if used in brewing, will become coated with proteins which should be removed from time to time with an enzymatic cleaner. If this isn't done the response of the electrode will slow. The junction frit can be replaced in some meters and this is a good idea too. But eventually the electrode just runs out of steam (slope degrades, response gets too slow) and it has to be replaced. Manufacturers make a big deal out of trying to speed response by things like clever junction design (I have one that renews the junction at every measurement), glass formulations and so on. Even so they take time.
Electrodes seem to be subject to hysteresis or to at least have a mind of their own. Sometimes the response is quick and some times it is slow. You must make the decision as to when to take the reading. Some modern meters take that responsibility from you and have an algorithm that freezes the reading if it doesn't change by more than x pH in y seconds. Some let you set x and y or one or the other. You must be very careful with this. In the lab I have the meter send it's readings to the computer where I plot them and print them to the screen as they come in. I can, thus, graphically see the change in pH over time. If the computer asks the meter for a reading when the meter thinks the pH is stable it marks it with an *. I have screen fulls of data without * but in which the plot shows pH slowly approaching an asymptote. As noted above with your water I wouldn't expect that asymptote to be reached in less than about 3 days.