A fixed price is only fixed against a specification. If the specification says "tiling to bathroom" the price can move; if it says "600 × 600 honed travertine, laid on a torch-on membrane with a 48-hour flood test, to 2.1 m on all wet walls", it cannot.
Watch for provisional sums. A provisional sum is an amount the builder has guessed because a decision has not been made — usually on stone, sanitaryware or lighting. There is nothing wrong with one, but every provisional sum in a quote is a number that will change, and you should know the total of them before you sign.
Prime cost allowances work the same way for supplied items. If your quote allows R1 200/m² for tiles and you choose tiles at R2 400/m², the difference is yours to pay. Ask for the allowance rates in writing and go and look at what they actually buy at a supplier before you agree.
The four words to search for are "subject to site conditions". They are legitimate in a demolition line and dangerous everywhere else. Ask the builder to name exactly which conditions and what the rate would be if they are found.
Finally, check the variation clause. It should require written approval and a revised figure before any additional work starts. If it lets the builder do the work and invoice afterwards, the price is not fixed, whatever the cover page says.