What happens with pH over time depends on the nature of the mash. It takes some time for whatever is reacting to react. If you have a mash to which you have added acid (in the form of liquid, powder or dark grains) some of that will be quickly released into the liquid and the pH will plummet and then rise over time as the liquid is absorbed by the grains and the acid reacts. If you add base the opposite will occur.
Agitation, of course, has a lot to do with this. There is a chart at
http://wetnewf.org/pdfs/estimating-mash-ph.html which represents a recording of pH over time in a test mash made by adding finely ground to a mixture of acid and water. You can see both the pH creep and the effects of stirring on the pH from that recording.
My experience in the brew house has been that where sauermalz is involved with minimal calcium the pH rises throughout the brew day having more or less stabilized after 15 - 20 minutes in the mash. My experience with more mineralized water has been that the pH stabilizes after about 20 minutes after dough in but then drops slightly after each decoction.
If you try to chase pH in the mash tun do it with liquid acid - not by stirring in powders, especially chalk. Powders are hard to mix, expecially if you have a thick mash, and the danger is that you will measure pH in a portion of the mash which the powder didn't reach or where the powder hasn't dissolved. If you want to use lime or baking soda dissolve them in a pint of water first and then add that pint in increments so as to no overshoot.
Better than trying to fix the pH in the mash is to know what it will be in advance. You can determine this by making a mini mash of about a pound of your grist (make sure it is well mixed) with a quart or so of the water (warmed to the proper temperature). Adjust the grist or the acids/bases added to the liquor, until the pH is where you want it to be. Then scale to the full brew. You ought to be able to hit the desired pH to within ± 0.05 units this way. Don't worry about being off by that much. Keep good records and use a bit more or less acid next time to try to 0 in. Variations between lots of malt will swing you about a bit but with experience you will be pretty close to what you want at each brew.
Starting off with a pH meter presents some frustrations. As with any new piece of equipment there is a learning curve. I suggest that people ascend that curve as far as possible before brew day. There are some comments on the proper use and calibration of pH meters at
https://www.homebrewtalk.com/f128/ph-meter-calibration-302256/ and even more details on what the meter does when you calibrate it at
http://wetnewf.org/pdfs/ph-meter-calibration.html. The instructions that come with the meter should be followed if they conflict with the instructions at the link I just gave.
Calibrate your new meter and go about the house (kitchen mostly) measuring the pH of orange juice, vinegar, milk, baking soda solution, household bleach, beer etc. You should be able to find generally applicable pH values for these on the web. Then turn to measuring the pH of bits of crushed malt in water.
Sometimes your pH meter will give you a surprising answer and the art of using one lies in being able to detect a suspicious reading. If you get an unexpected reading immediately rinse the electrode with DI water and immerse it in pH 4 buffer. If you don't read 4 (or close to it) recalibrate. Many a brewer has 'corrected' a calibration error in his meter by acidifying or alkalizing a mash.
Don't let me scare you with this. A pH meter is an invaluable tool once you learn to use it.
