Without a rehydro label by a certified testing facility saying it was tested doesn't mean anything.
The 13 ci tanks usually fall into an odd category of cylinders as the hydro law doesn't apply to cylinders of a certain material type and if they fall under the '2x2 rule'. Which means a cylinder under two inches in diameter and less then two feet long is technically hydro exempt and may also mean it has an unlimited life span as long as it continues to pass hydro.
However, a field can use it's discretion to refuse to fill said cylinder even if it falls within the DOT ruling. Also it is still recommended the cylinder be tested at least every 5-years even though technically metal cylinders are usually 3-year hydros.
So really you have to cross reference the DOT number and the material number that should be stamped on the cylinder and check the DOT and manufacturer website and see what it falls under and it's exemption status, if any. As well as the life span, be it limited or unlimited.