Because there's still the same total amount of money in the system, (inflation adjusted) prices can't go up too much. According to the Econ 101 model, goods with a fixed supply will probably get more expensive since there are more potential customers wanting the same amount of stuff, but goods with an extremely flexible supply will get cheaper, again, because there are more potential customers to spread the fixed costs over.
* There's also a sort-of-UBI variant where the funds come from monetizing some big nationalized resource and distributing the proceeds (e.g. the Alaska Permanent Fund Dividend). In that case the above doesn't apply, but neither does your fear. Since in that case the pool of money is dictated by the market value of the resource the voters can't directly impact how much they'll receive.
You cannot continually raise the UBI, as this is economically untenable, however there will be significant pressure to raise it every time there is a vote. I haven't seen any UBI proposal that addresses this.
Plus there is another real issue with a true UBI: inflation. If everyone in the US made $100,000 a year then an iPhone would cost $8000 instead of $800 as people could afford to pay more and Apple would adjust their price accordingly. How do existing UBI schemes plan to avoid this?