Hi Michael,
Websites can drive traffic pretty quickly with the right marketing with it.
SEO is very specialist and quite expensive generally. A monthly commitment normally for 3-6months. If they've promised you page 1 they're lying. No SEO expert can promise that. It's an educated guess.
Depending what the keywords are will depends how long it take to rank. SEO is a long term strategy though. Decent SEO work probably takes a month to carry out, link building etc and a further 4-8 weeks for google to find the links so you may not necessarily be moving anywhere quickly.
The keywords play a big factor. Some SEO 'gurus' (hate people who call themselves that), will show results by ranking you quickly for a search term with practically no traffic and no competition. Looks great on the face of it to the customer but in reality it's a complete waste of time. I hope they carried out some keyword research for you and provided the results so you could see the stats.
If you want to discuss how much you paid, what you paid for and the keywords you are using, I can run them through my software to see what they're like traffic wise for you if you'd like? Completely complimentary.
P.S I hope your site isn't on Wix/weebly etc or your wasting your time.