Should I have an overflow bottle?

I am still trying to learn about my Mopar I bought.
I have a 1971 Valiant, with a slant 6, auto.
The rad and water pump were brand new when I bought it a few months ago. No thermostat is installed right now. And the heater core is disconnected.
I bought my new heater core and thermostat. The last guy left the thermo out, so the engine could keep being flushed.
The car sat for about 14 years.
Anyhow. There is no overflow bottle. The hose just comes from the top off the neck, and goes down in between the rad and core support and hangs there.
I don't really see where an overflow bottle would have really went, unless I am just not understanding something.
I flushed the other day again, and filled it up to the top. I drove it today, and both places I stopped, it spit water on the ground. About a 8 inch circle. Is this normal? I mean I know I don't want to spit water everywhere I go. I couldn't open when I got back to see how low it went. Any tips? Or do I need a bottle?