Pears, I suspect your confusion arises from a concatenation of different time periods, places, rose cultivars and extraction methods throughout history. Let's see if we can untangle the threads a little. You may take any or all of this for whatever you think it's worth.
Rosa x damascena (literally, 'rose of Damascus') is a hybrid derived from a cross between Rosa gallica and Rosa moschata. Its precise origins are lost to the mists of time, but it is definitely believed to have originated in the Middle East. It has been associated with the city of Damascus in Syria for hundreds of years. It's unclear when this rose was introduced to Europe; some believe it was in Roman times, some believe it was brought back to Europe by the Crusaders, and others believe it didn't come to Europe until the Reformation. In any case, it was very likely known in Europe by about 1600.
Rosa x centifolia is a different rose hybrid, with Rosa x damascena believed to be one of its progenitors. It seems to have been developed by Dutch rose breeders, sometime between 1600 and 1800. Incidentally, Grasse's perfume industry really got going in the 18th century. It's tempting to speculate on how much the introduction of Rosa x centifolia, which must have adapted supremely well to the soil and climate of the CĂ´te d'Azur, fueled that development!
My understanding is that the word "otto" was a Latinization, or Anglicization, of the Arabic "attar", which means a precious floral oil distilled, specifically, into sandalwood oil. Because of this prerequisite, production of true attars has been traditionally done only in the Middle East and especially India. Over time and European use and custom, the word "otto" has acquired a meaning of its own, independent from the presence of sandalwood oil.
My understanding is also that an absolute is extracted using hexane or some other solvent. I believe this process began to be used in the West, but I'm not sure when - probably sometime during the 19th century, I'd guess. It was also, interestingly, during this century that roses for perfume production began to be grown in Bulgaria. But by the 19th century, global trade and advanced technology allowed plants and extraction methods to travel beyond their traditional borders.
Rose essential oils, ottos, attars and absolutes are all natural products, and will therefore smell different depending on the place where they were produced, the variety of rose, and the precise conditions of cultivation, harvest, extraction, and storage. Incidentally, this is why many production perfumers prefer to work with synthetics, but many hobbyist and DIY perfumers prefer natural products; variability can be a blessing or a curse. But a few general conclusions can be drawn. Those who have many different natural rose products to sample from often notice a "cooked" note from simply distilled essential oils or ottos; attars have a deep woody dimension from the sandalwood; and it is said that absolutes, because of the lack of heat in the extraction process, smell the most like the living rose flower.
So, Pears, I suspect that definitive answers to your questions - "I've read that rose otto is made with Rosa damascena but has this always been the case or was Rosa centifolia also sometimes used? " and "So they've historically made rose otto in Provence and not just rose absolute?" - depend on what you mean by "otto", what time period you're specifying, which variety grew well in which areas, and what technology was available at the time & place of extraction. Fascinating questions all, that truly lead us down the perfumery rabbit hole! For practical purposes, I wonder whether there's something you're specifically looking for, or whether you're just curious about varieties of roses. If your budget can handle it, you might want to try investing in a variety of different rose products from different places and produced using different extraction methods. I understand that today's CO2-extracted oils reproduce the scent of the living rose more faithfully than anything else to date. Unfortunately, they're nowhere near cheap!