Yes you pay taxes on ALL the stock sold no matter what the proceeds were used for... in your situation you sold some stock to pay for the taxes on all of the stock purchased/received. This sets the cost basis of the stock you kept ... so now you will only pay taxes on the profit of the stock kept to sell later.
For instance you got 100 shares of stock worth $10/share ... you had to pay the tax on the RSU 100 x $10 = $1000 basis and the tax owed was say $200 so you sold off 20 shares @ $10 share to pay the tax bill... this is reported on both the W-2 and the 1099-B. This leaves you with 80 shares with a cost basis of $800. When you sell those 80 shares say for $900 later you will only pay tax on the profit of $100.
