Indeed, your assumption is correct.
The "sarcastic/ironic" element is mainly conveyed by the use of "wohl", and in particular through the fixed combination of "da ... wohl ...".
One could also say
"Da hast du dich wohl zu früh gefreut!"
, translating roughly as "You rejoiced too soon! (with the connotation of "I told you so/I suspected that already"). So the element "jemand" is not strictly necessary, the construction can also be used without it in different contexts.
As Pollitzer mentioned in his answer, the phrase can of course also be used without an ironic connotation, describing an assumption.