Apparently, Bitcoin Core 0.13 will download part of the blockchain again, even though 0.12 already saved it on the disk.
My debug.log
shows the last block it downloaded with 0.12:
2016-08-15 09:07:28 UpdateTip: new best=000000000041eb2ccd0ed06d5bb632cf27b7ed584a669660cac28e1b71973720 height=922283 log2_work=67.979045 tx=10868067 date=2016-08-15 09:02:06 progress=1.000000 cache=7.3MiB(3942tx)
Later, some relevant excerpts from the debug.log
:
2016-08-15 09:40:14 Bitcoin version v0.13.0rc3
[...]
2016-08-15 09:40:28 LoadBlockIndexDB: hashBestChain=000000000041eb2ccd0ed06d5bb632cf27b7ed584a669660cac28e1b71973720 height=922283 date=2016-08-15 09:02:06 progress=0.999999
2016-08-15 09:40:28 init message: Rewinding blocks...
[...]
2016-08-15 09:47:48 UpdateTip: new best=0000000000211a4d54bceb763ea690a4171a734c48d36f7d8e30b51d6df6ea85 height=828576 version=0x20000000 log2_work=67.431752 tx=10111478 date='2016-05-12 19:05:48' progress=0.997200 cache=3.1MiB(7756tx)
2016-08-15 09:47:50 UpdateTip: new best=00000000000f0d5edcaeba823db17f366be49a80d91d15b77747c2e017b8c20a height=828575 version=0x20000000 log2_work=67.431752 tx=10108953 date='2016-05-12 19:05:43' progress=0.997200 cache=3.3MiB(9069tx)
2016-08-15 09:47:52 UpdateTip: new best=000000009c9e433e9a79e5b9e42c80848978d76c7078e0d35c706eea35dc4602 height=828574 version=0x20000000 log2_work=67.431752 tx=10106552 date='2016-05-10 19:28:48' progress=0.997141 cache=3.6MiB(11260tx)
2016-08-15 09:47:52 UpdateTip: new best=0000000000002fa99e0fa83ba05aa380f392c625e11807018c7ab2f84f773331 height=828575 version=0x20000000 log2_work=67.431758 tx=10106553 date='2016-05-10 17:32:25' progress=0.997138 cache=3.6MiB(11261tx)
[...]
2016-08-15 09:47:53 UpdateTip: new best=00000000004f22c4274b2358897f2b4abf001918629e241130fd3d1eafc4bfe6 height=829552 version=0x20000000 log2_work=67.44607 tx=10117642 date='2016-05-13 07:36:33' progress=0.997218 cache=4.4MiB(13128tx)
2016-08-15 09:47:53 UpdateTip: new best=0000000000f6287b3a4e30d86b07733862a6d5da4c00a897e2958f3831a6c6e8 height=829553 version=0x20000000 log2_work=67.44607 tx=10117643 date='2016-05-13 07:56:35' progress=0.997218 cache=4.4MiB(13129tx)
So apparently it was rewinding the blocks on disk and then reading some of them again from disk. Right now, it is fetching from the network, though.