If it only says SPDT, it should be on-on. On-off-on is more of a specialty switch, so it should certainly be spelled out in the docs if it is used.
A SPST is always an on-off switch. It only has two contacts, so it can't have two on positions. Although a SPDT is usually used, with only two terminals connected, where a SPST is called for. In this case, an on-on SPDT makes a good SPST switch.