I have not used this program myself, however as long as you meet the conditions (and there are more than just what you've stated) then you should not expect to have any problems.
Many airline check-in staff will be aware of the program, however even if they are not it doesn't matter. Airlines verify entry requirements for a country based on systems such as "Timatic" which provide details of what a passenger requires to enter a country, based on their nationality. The Timatic entry for a Vietnamese citizen entering Ireland from Timatic is included (in part) below. The airline staff will consult this output, and if you meet the requirements listed you will be allowed travel - regardless of whether they are specifically aware of the visa waiver program.
Relevant details from Timatic are :
Nationals of Viet Nam with a short stay visa issued
by the United Kingdom if they have first entered the United Kingdom
and been granted a stay of 180 days in the United Kingdom. They are
visa exempt for a maximum stay of 90 days in Ireland (Rep.) or until
the end of the period of stay granted in the United Kingdom, whichever
is shorter. Information: Passengers arriving in the United Kingdom,
including Northern Ireland, and traveling to Ireland (Rep.), the visa
waiver programme will apply and only a visa issued by the United
Kingdom will be required. The visit to Ireland (Rep.) must be within
the stay granted within the United Kingdom. Passengers are permitted
to travel to a third country before traveling to Ireland (Rep.) if the
visa issued by United Kingdom is still valid. Furthermore, re-entry
into Ireland (Rep.) from a third country is permitted if the visa
issued by the United Kingdom is still valid and period of the stay
granted in the United Kingdom is still valid. Passengers with a long
term visa must visit Ireland (Rep.) within a period of the current
stay granted in the United Kingdom.
Passengers arriving first in
Ireland (Rep.) and traveling to the United Kingdom, including Northern
Ireland, and then returning to Ireland (Rep.) will require separate
visas issued by Ireland (Rep.) and the United Kingdom. However the
visa issued by the United Kingdom will be accepted under the visa
waiver programme for the return journey to Ireland (Rep.).
Information: Not applicable to short stay visas issued for the purpose
of transit, marriage or to enter into a civil partnership.