By depositing the funds into a savings account, you caused this portion of your distribution which was apparently intended to be directly rolled over to another retirement account to fail to be rolled over. If you did not complete an indirect rollover of this portion within 60 days, the distribution became a potentially taxable distribution as you suggested.
In all likelihood, the payer issued a code G From 1099-R reporting a nontaxable direct rollover. Under the circumstances, the Form 1099-R is incorrect. Since the payer did what you asked as far as initiating the directly rollover, there is no reason to expect them to accommodate you by issuing corrected Forms 1099-R. Instead, you will have to create two substitute Forms 1099-R (Form 4852) to report the actual distributions and rollover that occurred.
Since two checks were issued it seems likely that some amount of the total distribution was after-tax money reported in box 5. If that's the case, the details of the two substitute Forms 1099-R are complicated to determine. For a single distribution split between two destinations, the law says that the first amount rolled over consist of the pre-tax portion of the distribution and only after the entire pre-tax portion is rolled over does any of the after-tax money get rolled over. Without knowing the exact details of the original Form 1099-R, the amount that was successfully rolled over and the type of IRA account to which the successful rollover occurred, it's impossible under these circumstances to determine the actual taxable amount and the necessary details of the substitute Forms 1099-R.
Presumably the distribution came from a qualified retirement plan (the IRA/SEP/SIMPLE box not marked on the Form 1099-R), not from an IRA. If so, these distributions are reported on Form 1040 line 16, not line 15. Line 15 is only for distributions from IRAs.
