Whether something is durative or instantaneous isn't a property of verbs, but of predicates:
- 「道を行く」 is durative
- 「うまく行く」 is durative (as @user4092 nicely pointed out)
- 「〇〇を買いに行く」 is instantaneous
With a durative predicate, you get these interpretations:
progressive
仕事は(今)うまく行っている
"My job is going well (currently)."
state
/ \
ーーーー|||||||??????????>
^ ^
begin now
going well
habitual
仕事は(毎日)うまく行っている
"My job is going well (every day)."
_______state_______
/ \
ーー||ーー||ーー||ーー||ーー||ー>
\ /\ /\ /\ /\ /
d1 d2 d3 d4 d5
note: this habitual makes it explicit you are currently in the state of this action happening habitually, while the plain-form habitual does not make that explicit
perfective
仕事は(今までに二回)うまく行っている
"My job has gone well (twice up to this point)."
_______state_______
/ \
ーー|||ー|||ーー??????????>
\ / \ / ^
1 2 now
With an instantaneous predicate, you get these interpretations:
resultative
父は(今)タバコを買いに行っている
"My father is out to buy cigarettes (currently)."
state
/ \
ーーーーx||||||??????????>
^ ^
go out now
habitual
父は(毎日)タバコを買いに行っている
"My father is going out to buy cigarettes (every day)."
_______state_______
/ \
ーーx|ーーx|ーーx|ーーx|ーーx|ー>
\ /\ /\ /\ /\ /
d1 d2 d3 d4 d5
perfective
父は(今までに二回)タバコを買いに行っている
"My father has gone out to buy cigarettes (twice up to this point)."
_______state_______
/ \
ーーx||ーx||ーー??????????>
\ / \ / ^
1 2 now
Generally, people explain that the difference between durative and instantaneous predicates is that a durative predicate gets a progressive interpretation (in addition to the other two), while an instantaneous predicate gets a resultative interpretation (in addition to the other two).
I agree with that explanation, but I hope by comparing the pictures of "progressive" and "resultative", you can see how they are pretty much exactly the same concept, it's just that it's the action which is continuing in the "progressive" case, while it's the result continuing in the "resultative" case.
Your question
Your question really has to do with what that native speaker meant. The fact is that 「タバコを買いに行く」 is instantaneous and 「父は今タバコを買いに行っている」 has a "resultative" interpretation.
One possibility is that your native speaker source could have been saying that 「父は今タバコを買いに行っている」 can have the implication 「父は今タバコを買っている」, which is an action 父 is in the process of doing (though not necessarily -- while he went out to shop, he may instead be stuck in traffic or lost).
Another possibility is that your source did not properly convey what they meant, and they were only try to say what the "resultative" picture (and "progressive" picture, in fact) says, namely that the subject is in some on-going state.