Are you sure your TWS chart shows "last trade prices" and not something like mid-point data? The average of 1.07350 and 1.07355, rounded to five digits, would show up as 1.07353. You can check under Edit -> Chart Parameters for your chart window.
If the instrument's mintick is 0.00005, historical data bars should never show values ending in 3 or 9. You should always get prices that are integer multiples of mintick.
Exactly which real-time feed gives you prices ending in 2? Some of the real-time data feeds and related historical data requests (such as TickByTick LastAll and RtVolume) may get funny prices but those records would generally be tagged as "unreportable" or have some kind of special designation that relate to institutional trade or special situations.
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