Finally did some research and here's the result:
In order to get your other puppets to wear the wedding outfits beside your starter,
you need to have your other puppets to increase 99 levels in order to get the heart mark to appear on the bottom-left screen of your Puppet profile and that means
you need Reincarnation in order to do so. But it is possible for a level 2 wild puppet to reach level 100 to get the heart mark even before postgame. You don't have to get all S ranks to activate though.
Example:
1. This is a reincarnated Lily with mediocre stats.

2. Using Native Grace (given by Suwako after you beat her), and fought one of the Hell Fairies in the tower at Hecatia's Hell by switching Lily for full boost EXP with my Lv100 puppet.
Lily increased around 46 levels with Native Grace EXP boost. Then I reincarnated Lily again and repeat the fight for another instant level Lv46 gain.
Bringing a total of 92 levels. That's 7 more levels for the heart mark to appear.

3. I reincarnated her again and doing a random wild puppet battle and once Lily reached lv.8, reaching over 99 levels goal, a heart mark appeared and Lily can now wear the wedding suit!

Note: Let's say, you caught a level 16 puppet and now a level 82 puppet and you decided to reincarnate him/her back to level 1. Since you have 66 levels gain (82 - 16 = 66), then you need another 33 levels to achieve 99 levels for the heart mark to appear. By the time your reincarnated puppet reached level 33, a heart mark should appear.
PS:
I did another test for Rinnosuke. lol how handsome. XD
