Asiana to Asiana international to international in T1 is MCT 45 minutes https://flyasiana.com/C/US/EN/travel/airport

Many people do this every day -this is how Asiana and Korean Air both make their money with transfer passengers an hour or less on many an itinerary.

and if your flight is that tight, someone will meet you at the plane door to escort you directly. You can also ask the flight attendant to move you to the front to when they prepare for landing to get off faster. Also, if you're in the transit security line - you can show your boarding pass to the staff and they'll let you through without a wait.

Not to mention Asiana won't board any flight until 30 minutes before departure anyway, and they hold planes all the time for connecting passengers.