It has been my practice, and the practice on most genealogy sites, to use the current name and location of a place in order for all users to be able to find it on current maps. The fact that a country didn't exist at any given time becomes irrelevant as we know, and as you suggest, as the name of the country or the empire it was included in (Austro-Hungarian, Russian, etc.) changed frequently over time. So, for the case of Turady it should be recorded as: Turady, Ivano-Frankivsk, Ukraine. Then, if you want to refer to it as it existed in an earlier time period, you can refer to the empire it was part of at the particular time.
Also, as an FYI, the country of Ukraine does not need to be referred to as 'The' Ukraine, as it is not a region, like 'the prairies', or a collection of states, known officially as the United States of America, or the Netherlands. Calling it 'The Ukraine' would be like calling Canada, "The Canada".