Hi Eminor,
What you are seing is clearly the nitrogen cycle kicking off again. You will always have a cycle, or if I may call it a "mini-cycle" when you start a new tank even with a cycled filter. In your case it's more pronounced and here it is why:
1. You cleaned the filter sponges and disturbed the bacterial assemblage and balance thus reducing the amount of bacteria present in the filter and how they work;
2. I assume you are using a new substrate since you say it's a new setup, and even if the substrate is inert, your filter bacteria needs to repopulate and adapt to the new water chemistry so there will be some instabilities for a while. Also, and most importantly, keep in mind that in a planted tank, most of your bacteria resides in your tank substrate really, not your filter so by simply using your filter on another new setup you effectively removed the majority of bacteria present.
3. Plants are settling in and may experience transitioning weakness which will further allow algae to proliferate.
I'll give an advise when doing a new tank with a cycled filter. This will not totally eliminate the cycle but will reduce it's effect. Never clean the filter when starting a new tank. Wait a few weeks for the tank to settle, then clean the filter. Also, keep a good amount of water from the previous tank and use that in the new one. If possible, re-use the old substrate partially (maybe 20% or so) as a base layer to inoculate the new substrate and speed up the colonization process. When doing it this way, you will see less of an impact, although if you are using brand new ammonia rich substrate, you will still go through a cycle, albeit a shorter one compared to starting from scratch, but if there is some ammonia release, you will not be able to void it. In my experience when doing it this way you can see 0 ammonia/0 nitrite in around 4-5 days and doing heavy WC every day. If using an inert substrate, the cycle will be much shorter but you could still have some algae taking advantage of the temporary instabilities. That's exactly what algae looks for.
Good luck with the new setup. It should be fine in 2 or 3 weeks as long as you properly maintain it. Remove all the algae you see. Don't let it settle.