I have been trying to get this right and I just can't seem to nail it.
I have set up the first rule and it seems to work, moving new MEMBERS group, joined <1day ago, to a TRIAL secondary group.
But when the user purchases the product that moves them in to the PREMIUM group, I cannot remove the TRIAL from secondary according your second rule above.
Products do not allow you to *remove* secondary groups as a benefit, only add them.
And, I think because of the highlighted part here, group changes from products do not run group promotions...