Martin was arb-eligible, not free agent-eligible. Being arb-eligible, he had the right to reject the contract that the Fodgers tendered him and opt for an arb hearing. The Fodgers didn’t want to risk paying him what he might have been awarded in arb, so they never even officially tendered him a contract (hence the term non-tendered). When an arb-eligible player is non-tendered, he immediately becomes a free agent and he doesn’t even have to pass through waivers.

Free agency arb works differently. All players (that are past their arb years) whose contracts expired after a given season have a certain number of days after the WS is over (this year it was only 7 days) when their former team has exclusive rights to negotiate with them. If they don’t sign, then they become official FA and can negotiate with any team. Their former teams have a certain number of days (this year I believe it was 22 days) to decide on whether they will offer arb to the FA. If they do offer it, and the player accepts (he had 10 days to decide this year), then the player belongs to them for 1 year (the contract amount is decided by an arbitrator at a hearing in January). I they do offer arb and the player rejects it and signs with another team then his original team gets compensation (2 picks if he was Type A and 1 pick if Type B). They player can also sign with another team before the arb offer deadline. In that case his former team is sure to offer him arb, because he’s already belongs to another team and their comp picks are guaranteed with no chance of the player gaining arb.