According to the CG Historian's official website the Smilax was commissioned in 1944, the Eagle on May 15th, 1946.
Acushnet was commissioned as USS Shackle by the Navy in February 1944, decommissioned from the Navy and commissioned into the Coast Guard as USCGC Acushnet in August of 1946. Smilax should have had the title of oldest commission (November of 1944) all along if they're going by CG commission date, with Eagle (May of 1946) second and Acushnet third. If they're counting original commission date regardless of service, then Eagle's got them all beat by several years with its 1936 commissioning as SSS Horst Wessel, then Acushnet/Shackle, then Smilax.
Timeline:
USCGC Eagle first Commissioned (as SSS Horst Wessel): September 1936
USCGC Acushnet first Commissioned (as USS Shackle): February 1944
USCGC Smilax Commissioned: November 1944
USCGC Eagle recommissioned: May 1946
USCGC Acushnet recommissioned: August 1946
The only way it makes sense to put Acushnet first and Smilax second is if you're going by total US service, regardless of branch or name.