The reading of your rights is from Miranda v Arizona.
It's not like TV though.
They only have to read the to you before they attempt to interrogate you as a suspect in an intimidating setting, like a police interrogation room.
The OP is likely to have either confessed while being arrested, or gave the officers enough evidence during the arrest that they did not need to interrogate him at the station.
The Miranda ruling does not give you any rights. It only requires that police inform you of you rights in certain settings. At any time, before during or after your arrest you can exercise those rights.
If the officer asks you any question after you have requested a lawyer without council present, he can be held criminally liable for infringing on your right to council. However, after you have requested a lawyer, if you begin speaking to the police, they can question you again without a lawyer present.
The only words you should ever say to a police officer are, "Am I free to go?"
If he says no, you shouldn't say one more word, except to ask "Am I being detained?" And if you are being detained say you do not consent to any search and you would like a lawyer present before questioning, don't speak one more word. Be very respectful. Respectfully establishing your rights while being understanding of the officers job can go a long way to get on the officers good side, while blocking every avenue he has to keep you detained or gain evidence from you.
If they say you are not being detained, ask them "Am I free to go?" Loop this around until they either say you are being detained or you are free to go.
This is not legal advice, just my experience with it.
"Tu ne cede malis, sed contra audentior ito."