27.8 vac from the second floor transformer is fine and quite common, (that is because the primary voltage varies by 5 to 10% daily, and also the specification might be 230 volt transformer and a 240v primary transformer is not available....)
Some of the counter men at the wholesale houses are quite new to the business without any hands on experience.. those get paid about a quarter of what an experienced high quality tech gets... taking their advice will often get a person in trouble.
Regarding your comment:
"I changed the transformer and installed the new one. Again 27.8 going into the transformer and something like 24-25 volts? coming out."
That is now how we measure it, the one and only measurement that counts is **between** the two poles on the secondary side. no reading from either pole (in and out to use your terms) are valid to prove transformer output...
a reading from each pole to ground is used only to prove if a transformer reads below 10vac or so, that is quite rare. we replace in that case.. there is no IN and Out on the secondary side of the transformer, that is AC current it alternates 60 times a second.
The only IN reading that counts is between Line1 and Neutral on the PRIMARY side of the transformer, the only OUT reading that counts is between the two poles on secondary side of the transformer.
Regarding power to the outside unit, it is *not live unless you get 230v **between** line1 and Line2... readings from either line to ground showing 120v do not count.
Its time to locate the "finish and rate" link now, I will appreciate that, and in exchange will hold the question open for any follow up you need in the event the tech you called is not one the more fortunate ones in the top 20% of his field.