It doesn't make much difference if you are overlaying the OSB with backer board as you indicated. By "backer board" I assume you mean something akin to 9/16" glass mat cement backer board. With this overlay the mortar shouldn't reach or affect the OSB. The backer board will also stiffen the subfloor system which, in turn, will reduce deflection and subsequent cracking. This stiffening improvement is perpendicular to the joists, and doesn't help deflection along the length of the joists.
The Tile Council of America has an installation specification (F155-03) for tile floors over OSB decking but it includes covering the OSB with 5/8" exterior plywood. OSB has come a long way in the past 20 years but still isn't generally accepted for applications in direct contact with wet materials and this includes mortar (even though it cures to a dry state). Some of the earlier OSB was easily damaged by moisture.
A separate issue is deflection. This is the amount of "flex" in a floor system. When the weight of people and equipment are applied to any floor some amount of measurable deflection occurs. Wood and vinyl materials can tolerate an enormous degree of deflection without defect or failure. On the other hand, tile isn't nearly as tolerant. Deflection limits are measure by the formula l/360 where l = the span of the floor (distance from end of joist to end of joist) in inches divided by a three digit number. The lower the 3 digit number the greater the deflection. Wood and vinyl can easily cope with deflections of l/180. Ceramic tile requires deflections of l/360 or better to prevent cracking. For this reason plywood is more often used than OSB for decking because plywood is slightly stiffer than OSB when applied in the correct orientation (grain perpendicular to the joists). Whether using plywood or OSB, the floor must be stiff. Thus the thicker the decking the better. If your floor joists span 10 feet they should not deflect more than l/360 or 10' x 12" / 360 = 3/8 inch when a 300 lb. load is applied at the center of the span. The 300 lb. load is an arbitrary amount but is the load used by the Tile Council of America.
If your floor deflects more than the limits described above, you need to stiffen the floor by 1) adding extra floor joists or 2) shortening the span of the floor joists by adding a wall below at midspan or 3) installing a heavier deck or a combination of the three. Although a heavy decking is usually a desirable quality, it won't help weak joists very much. The best way to stiffen a floor in all directions is to add new joists between the existing joists. The added joists can be place midway between each existing joist (best method) or can be scabbed (sistered) to the side of each existing joist (easiest method). In the latter application the added joists are not required to sit on the support walls at each end as long as they are within a few inches and are well nailed to the existing joists for the full length.
Considering the time, energy, and expense of remodelling and installing ceramic tile, don't cheat on the foundation. In this case the foundation being the joists and decking. It is better to be too stiff than too flexible.
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