The demo went well because it was built to go well
The demo went well because it was built to go well: the vendor's data, the vendor's driver, and the three workflows they know by heart.
A demo is supposed to work that way. The risk is signing before the software has met your own orders. Without a test, that first meeting happens during setup, after the contract, when changing course costs real money.
Your business lives in the exceptions. The customer who pays half up front and half on delivery. The order that ships from two locations. The price that is different for one account. The job cancelled after the parts were ordered.
Before you sign, send the vendor twenty of your real records, and pick the messy ones on purpose. Ask them to run those through the system while you watch, with the employee who does that work every day sitting next to you.
Then watch your employee. Every time they say "and then what happens when", write the question down. Each one is a setting to find, a gap in the software or a change order waiting to be priced, and you want to know which before signing.
If the vendor cannot run your records before signing, ask what they can do instead, such as a short paid trial on a copy of your data, and get the answer in writing.