This evening before doing a mission with my warrior, I logged with one of my mule character and found a 1st year birthday present.
Opened, fungal wallow - well I have a couple of them already, anyway ...
Finished mission, I wanted to place some items on a mule, the previous was full, logged to another and found another 1st year birthday present.
Opened, fungal wallow

Bleah, very bad luck, 2 in the same evening.
Did another mission with my friend to help him in Tyrian guardian, then I took my dervish because I bought some scythe upgrades and wanted to use them.
My dervish had his 1st year present ...
My friend offered himself to open for me, I thought that was not necessary, opened myself ...
Fungal wallow.

Three in the same evening on the same account. It is possible that it's a coincidence, but it's not likely at this point.
The 3 characters were not created in the same day, it's possible that some presents had been there for 1 week or more.
All the 3 of them had been parked in the same place (guild hall) for 1 month at least. I opened the 3 packages there, with an interval of half an hour each.
In my opinion, the day/hour and the place where you are when you open (or get?) the present are in some way taken into account by the "random" generator.
After my experience, this "randomness" is a bit suspicious.
I don't complain about the quality - with the exception of Mallyx and asians I already have dozens of minis, mostly bought with exception of Lich and Djinn which I received on my characters - but I'm just not convinced about the fact that the random generator is really random.