Technically speaking the second arrest and conviction can be considered if a violation of a conditional discharge violation is filed against you. The DA probably did not say anything because they either did not realize the possible violation of the conditional discharge or they did not care about the earlier conditional discharge.
Again, technically speaking the district attorney can bring back the original case as a violation of a conditional discharge. Odds are the prosecutor will not do so and you should relax.
Note: For informational purposes only.
generally, it very well may be that the DA simply didnt care to reopen the prior case. They do have a right to file a Violation of the Conditional DIscharge (VOCD) but for the most part they may well feel that it would be a wase of time to ropen that previous matter.