In my opinion, it doesn't occur; while I have read, some papers and chapter of books which show it might occur in some special processes and conditions.
If the temperature of the melting titanium during the process: like welding (the process being tested by myself), etc., does not go beyond the temperature of the titanium transmutation (phase change temperature), the beta grains do not begin to grow on the grains boundary.
What alloy are you working with? A commercially pure titanium or an alpha alloy behaves differently than an alpha-beta alloy or beta-dominate alloy.
The alpha-beta transformation is allotropic and occurs at ~890C whereas melting in pure titanium occurs at ~1670C.
Any process that will heat an alpha titanium above this transformation temperature (even in small areas) will cause a local transformation from alpha to beta phase. This will not just be at the grain boundaries but rather the entire heated grain to transform into beta. Upon cooling, the transform will reverse if beta is not stable at room temperature (as in the case of Alpha-alloys). Beta is not typically retained at room temperature unless alloying stabilizes it.
Any welding process necessitates that melting temperatures are achieved near the fusion line and it rapidly drops off from there. Therefore, you will exceed the transform temperature irregardless of the welding procedure you use in at least a small localized area.
This means you will see the formation of beta phase in the fusion zone, the deposited weld metal, and the heat affected zone during welding. Whether or not that beta phase stays depends on the alloying. If cooling rates are fast you can see the formation of martensitic alpha prime phase in the heat-affected zone rather than pure alpha phase. This phase transformation can occur from strain.
In summary, if you are using a CP-Ti or an alpha-alloy you are likely to get alpha-Ti and possibly martensitic alpha prime through this process at room temperature in the final microstructure. At elevated temperatures, the entire heat-affected portion of the base metal that is not melted (anything above ~890C but below the melting point) will become fully beta phase and reverse upon cooling. The solidifying liquid metal will form beta first until the transformation temperature is reached then all the beta will transform to alpha and/or alpha prime. Retention of beta at room temperature is a function of the alloying since it must be stabilized.