And to add my own data point as well:
Applied for no annual fee version (with bonus capped at 50,000 avios after $2000 spend in 3 months) on 2/16. Application went pending, but approved on its own on 2/18. On 2/18, sent SM asking match of 100K avios offer, and the match was approved on 2/19. As noted in other posts above, in the message approving the match, they mention that I need to let Chase know after I've met the $10,000 and $20,000 marks, so they can manually add the additional bonus at those times.