Usually Contractors give you an estimate (on paper), and they come to your home to assess the "job."
In my city, the estimates are free.
Then you pick them or not.
Stone tile, versus ceramic tile... are 2 very different things.
Stone, requires a certain type of sealer.
And if it is stained/dirty, on stone that was not previously sealed or the sealant was not kept up, then it has to be cleaned then sealed again.
Stone sealant does have to be reapplied every so often.
There are different types of stone, some being more porous than others.
ie: there is slate, limestone, travertine, marble, granite, quartz, etc.
And did he say how he would clean the stone? On the phone with you?
Did you tell him... you have STONE flooring? And what kind of stone?
If stone is very stained, (again, some stone is porous) sometimes it cannot be cleaned until it looks like new virgin unused stone.
The bottom line is: a "phone" estimate was given to you. The Contractor(s) did not come out to your home to assess the job. Thus, the Contractor could NOT give you an accurate estimate, of the job and per the type of flooring you have nor the solution to clean it etc.
Hence, once the Contractor did come to your home and saw the situation, the price of the job, changed.
Never.... get just a phone estimate for jobs like this.
Any professional Contractor, will come to your home first (or a professional Estimator comes to your home), to assess it... then give you an estimate. And at that time, the homeowner and the Contractor discusses what needs to be done. BEFORE you actually hire them.