Unfortunately, this is more complicated. For German investors, the dividends which an ETF reinvests must be immediately taxed as capital gains. For ETFs which are domiciled in Germany, *I think* this is done automatically. However, if an ETF is domiciled e.g. in Ireland, you must declare the reinvested dividends in your tax declaration, because the bank does not automatically deduct the capital gains tax. You can find the required information in the Bundesanzeiger, though I do not know where exactly the relevant numbers are stated.
Note that some synthetic ETFs can "swap away" the taxable gains, so taxation depends on the method of replication. You will find out in the Bundesanzeiger whether or not your ETF has generated taxable gains in any given year.
Another thing: The reinvested dividends do not increase your number of shares of each ETF, but they increase the value of each ETF share. As a consequence, when you sell your ETFs, your bank will deduct capital gains on the reinvested dividends *again*, as the bank only sees that the ETFs value has gone up since you bought it and interprets this as a capital gain, even if the increase in value was from reinvested dividends. You can get this money back if you prove that you already paid the taxes on the reinvested dividends; for this purpose, you need to keep all your tax declarations (or the Steuerbescheide?) until you eventually sell the ETF.
I think the whole procedure is quite messy, and I hope that it will eventually be simplified.