Where did Sparrow's compass really come from?

Reference to The Compass and Jack Sparrow's Compass

Did Dalma give the compass to Jack's former captain and eventually it reached Jack?

Yes.

The origin of this unique compass is shrouded in mystery.

Around the time of Jack Sparrow's quest for the Sword of Cortés, the compass would be in the possession of Laura Smith`, the captain of the infamous pirate ship La Fleur de la Mort. When she and the crew of the fishing boat Barnacle, led by Jack Sparrow, escaped from the Pirate Guard in New Orleans, Laura used the compass to find her ship, which was invisible at that time because its magical sails were unfurled. Sometime afterward, the compass would end up in the possession of the mystic Tia Dalma through mysterious circumstances.

At some point, Jack Sparrow would barter the compass from Tia Dalma years prior to his search for the treasure of Isla de Muerta.

It is unknown what Jack gave to Tia Dalma in exchange for the compass.

However, the compass somehow found its way into the hands of Morgan, the pirate captain of the Wicked Wench, under whom Jack was serving at the time. When Morgan was mortally wounded during the battle off the coast of the mysterious Devil's Triangle, he gave the compass to Jack, telling him with his last breath never to betray the compass.

We saw in Dead Men Tell No Tales, that Jack Sparrow holds the compass desiring something that would help him save the Wench and her crew from their attacker, the notorious Spanish pirate hunter Armando Salazar and his dreaded warship the Silent Mary, Jack took command of the Wench, steering her toward the Triangle. At the last moment, Jack tricked Salazar into sailing into the Triangle where all the Spaniards were killed in the explosion of gunpowder when the Silent Mary hit the reefs.

Cross posted from my answer on Sci-Fi.

I'm not sure exactly how canon it is but according to the Pirates Wiki page on the Compass:

Jack Sparrow's compass was an unusual navigational instrument most notably used by Captain Jack Sparrow, which he bartered from the voodoo mystic Tia Dalma and later inherited from his captain.

So apparently he bartered it from Tia Dalma, somehow lost it, gave it away, or alternative and then got it back in the flashback scene we see in Dead Men Tell no Tales.

The same page goes on to say:

However, the compass somehow found its way into the hands of the pirate captain of the Wicked Wench, under whom Jack was serving at the time.

So it appears to be unclear how the compass left Jack after he bartered it off of Tia Dalma till it comes back to him again.

So it doesn't appear to be a continuity error but more that both events happened with Jack bartering the compass from Tia Dalma. He then somehow loses possession of it, this part is a grey area, and lastly inherits it from the captain.