Your immigration lawyer here might be referring to the emails that IRCC sends when you have an update on your profile. But you do not receive emails for some ghost updates. You only notice changes when you log in to the profile. I feel you may have received a ghost update at some point after March 20. That would indicate background checks are starting. Maybe your immigration lawyer may have not noticed it.
Anyways, it is great that your eligibility has been met. That's surely a great sign and must be a huge relief from the stress. Your security should be quick since you shouldn't have any history so should expect good news soon
Honestly, I would relax if I were you because eligibility was biggest hurdle.