Thanks to Tim Verhoeven who pointed me towards the right direction.
I've checked 3ware web site, and found newer version of tw_cli, which worked. It also created /dev/twe* devices (I have an "older" 8006-2LP card, newer cards use twa* devices). That solved problem with tw_cli tool.
For smartd, I had to change /dev/sda to /dev/twe0 (I guess in the past specifying /dev/sda in smartd.conf worked too). However, than SELinux kicked in. The problem was that tw_cli created devices but did not set correct context for them (they inherited it from parent dir). Running restorecon on /dev/twe* solved the problem partially (on reboot, the devices were gone, of course). I've found some references that smartd was supposed to create devices on startup if /dev/twe0 is used in smartd.conf, but it didn't do it my case. Hm, maybe it does it for twa devices only, who knows... Anyhow, I solved both problems (device creation during boot and setting correct SELinux context) fast and dirty way, by creating nodes in /etc/udev/devices with correct permissions and SELinux context.
I've also found this relevant bug: https://bugzilla.redhat.com/show_bug.cgi?id=232218
Looks like the bug was resolved by hacking smartmontool. Though, I wish they went with original proposal and fixed the device driver instead, so that udev would automatically create devices during boot if 3ware card is present in the system.
Once again, thanks to Tim for pointing me into right direction.