As the plaster cures for the first year, you will experience an increase of pH levels (can last up to a year). You need to be diligent about keeping the pH in check so that you don't develop scale on your new finish. You also want to use a nylon brush on the surface when brushing, there's an article somewhere about the startup of new plaster I'll see if I can find it.
Tabs are a good way to keep the pH in check while chlorinating - it's not always a bad thing to use tabs LOL. I would recommend using at least a floater with tabs to assist in that regard, just make sure it doesn't get stuck in one location all the time... I'm not a fan of Pentair chlorinators so thus the floater suggestion.
If you would rather not use tabs, and an any event, you should keep plenty of muratic acid on hand for keeping the pH in check. You can use liquid chlorine for chlorinating, use the pool calculator to figure out the proper dose to add 2-4 ppm of chlorine each evening. You'll need to shop around for the cheapest price, regular bleach vs. pool store liquid for example. Once you know your % strength you plug that into the Pool Math calculator and you come up with your evening dose. Use the calculator to determine how much stabilizer to add, and I would suggest a nylon knee high in the skimmer.
You're pH, ALK and CH levels will change on their own for the first year so nothing should be added manually at first except chlorine and stabilizer.
Off to find that article for you...
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Pool School - How To - Start Up New Plaster