This is very strange that included bottle turned out to be too little for the system. On the other hand it's only 120mm rad. I you didn't spill itI will blame enormous length of tubing.
You can't use tap water, that for sure. Destilled or DI water is OK. Look and the composition of your coolant: if main ingredient is miscible with water I would say: dilute it. Remember that the color will not be as intense as straight from the bottle.
Before diluting wait for other advices/opinions - i may be wrong (even though I use DI water + CuSO4 x 5H2O since 2008)
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