Turkey and Armenia have strained relations for somewhat obvious reasons, but it's not on the same level as, say, Israel and the Arab world.
There have even been faltering moves in the last decade to try to heal the rift and ease towards increased trade, and where these have fallen down, it's been as much to do with pressure on Turkey from Azerbaijan (recently at war with Armenia and with an unresolved open conflict over Nagorno-Karabakh) as direct emnity between Armenia and Turkey. Opposition to rebuilding trade with Turkey on the Armenian side is stronger from the (influential) Armenian diaspora than it is within unemployment-ravaged Armenia itself - it's much easier to say "no compromise" when you're the other side of the world to where the consequences are felt.
For example, there were almost direct flights between Turkey and Armenia in 2013 - until the Azeris intervened:
Turkey has canceled the first ever scheduled Turkish flights to its long-time rival Armenia, days before the first plane was due to take off, officials have said, following fierce opposition from Turkey's ally and energy partner Azerbaijan.
The twice-weekly flights between Turkey's eastern city of Van and the Armenian capital Yerevan were due to begin on April 3 and, encouraged by a U.S. push for rapprochement, were meant to boost bilateral tourism and trade.
It's possible to book flights from Turkey to Armenia (albeit via Russia, usually), and buses from Turkey to Armenia (albeit via Georgia).
Of course it's always possible you might encounter a particularly partisan individual border guard, who might use it as an excuse to make a fuss or try to obtain a bribe, but the airport is generally pretty professional by the standards of the region - when this sort of thing happens, it tends to be on the land border with Georgia. Such (relatively rare) situations can usually be resolved by staying calm, avoiding confrontation, and if necessary saying something like "I'm sorry, I do not understand. May I speak to your supervisor?".
In extreme cases, I've heard stories of people turning such situations around with a disparaging comment or vulgar joke about the country that is the source of the anger, but for ethical reasons it's best not to stoke and legitimatise this kind of nationalism unless you feel genuinely in danger and there's no obvious alternative. I've not known anyone feel the need to resort to this travelling into Armenia having travelled in Turkey, and definitely not in the airport - in fact, I think the incident I'm thinking of, they were travelling into Azerbaijan having travelled in Armenia. The wounds from the Armenian-Azeri war are much fresher and more raw in the Caucasus itself than those between Armenia and Turkey. You won't need to do anything like this in the airport in Yerevan.