No it should not crack significantly - sounds like maybe he did not reinforce it, or did not put in control joints to control where the shrinkage cracks occur. New concrete, unless abused, should not crack noticeably for several years at least. Cracking in 3 days probably means either too hot or cold when cast or in couple of days thereafter, watered the mix down, did not reinforce it, failed too properly cure it, or failed to compact subgrade properly before pouring it. Probably most common of these - watering down to extend workability time on hot days and failing to properly water cure for at least 3-7 days.
You should not have waited 4 months - you could try claiming against his bond. If they say it has been too long - especially if no warranty in the contract, then you are probably limited to suing - maybe in small claims court, if dollar amount of damages (replacement) is within small claims court limit and you have documentation, especially of your going around on this for 4 months with him.
