Tap water contains Nitrates and Phosphates along with many other things.
(I would suggest you invest in a RODI unit when finances allow).
Seachem Prime according to them:
* Removes chlorine & chloramine.
* Detoxifies ammonia, nitrite, and nitrate.
The phosphates are what is fueling your algae along with your tank being young.
Here is a good read:
https://www.asm.org/index.php/educa...trate-and-phosphate-levels-on-growth-of-algae
Coraline algae will take some time to appear. Its best to introduce it into your system.
This could be as simple as a snail or hermit with it on its shell or adding a small piece of live rock with it as well to help "seed" your tank.
As mentioned above your tank is still young and you need to get your phosphates and nitrates down and under control.
Its best to continue letting it mature. Your bio filter will become stronger and parameters will start to stabilize over time.
Test your water and perform regular, scheduled water changes and tank husbandry to help export some of those undesired nutrients.
When I first started out a few years ago I wanted the same thing. Now coralline is everywhere and can be a real chore at times. (careful what you wish for).
This hobby will force you to learn patience; at least IME.
This is what I found works for me when I want that purple on my rocks in newer tanks when they are ready.
I remove coraline off the class of one of my established/mature tanks while placing a fine mesh net in front of a power head to collect the shavings.
I then take those shavings and place them in a container/bowl with saltwater.
I dose that small amount of water with a large amount of Cal, mag, and alk and whisk vigorously. (Some people use a blender)
Then slowly poor the contents into a powerhead(s) of my newer tank.
Within 2 weeks I have spots of coraline popping up on my rocks and equipment.
Hope this helped.