Light with Dimmer and LED bulbs blinks when on by itself
Incompatible Bulbs
A modern dimmer (or timer or smart switch) needs to get some power from somewhere. That can come from:

Complete circuit using neutral in the switch box. These dimmers will say &quot;require neutral&quot;, have a white wire for neutral and include directions on how to connect it. Based on the installation manual, these dimmers don't use neutral. Neutral is the &quot;best&quot; technically, but because many older installations don't have neutral readily available in the switch box, many switches (dimmers, timers, smart switches, etc.) avoid using neutral.

Complete circuit using ground. These dimmers will say &quot;require ground&quot;. They use ground as a legal loophole for completing the circuit, since ground == neutral for all practical purposes. That is not permitted for other uses (e.g., receptacles, light fixtures, etc.) but is permitted for dimmers, timers, smart switches, etc. that are designed properly and that use the ground for very low levels of current. Based on the installation manual, these dimmers don't REQUIRE ground. Ground is shown in the diagram, but there is no mention of it being required. In addition, there is the following note:




When no “grounding means” exists within the wallbox for an existing switch or dimmer, the National Electrical Code (NEC) allows a switch/dimmer to be installed as a replacement as long as: 1) a nonmetallic, noncombustible faceplate is used with nonmetallic attachment screws or 2) the circuit is protected by a ground fault circuit interrupter. Lutron wallplates meet this requirement. When installing a control according to these methods, cap or remove green wire before screwing control into wallbox.


which means you can, if and only if ground is not available, install this dimmer without connecting ground. That would absolutely not be the case if the dimmer used ground to complete the circuit. **FYI, that means that, especially if you don't have a ground connection, you must use the included (non-metallic) screws instead of standard metal screws.

Battery power. Not ideal because batteries need to be changed periodically. This dimmer does not use a battery.

Leak current through the attached light fixtures. This is the only choice left, so this dimmer must be doing that. Unfortunately, this leakage causes problems with some LED bulbs. A dimmer-compatible LED bulb has to function properly in a number of ways that simply don't cause problems with incandescent bulbs. If the bulb is not truly compatible then you can get any/all of:

Dim light, flashing light, buzzing noises when on, particularly if at less than &quot;100% power&quot;.
Dim light, flashing light, buzzing noises when off.



Turning on additional devices on the same switch (e.g., replacing one LED bulb with an incandescent bulb) almost always changes the characteristics of the circuit enough to eliminate a lot of problems. Changing something else on the same circuit can have effects too, as you have discovered. It doesn't make a whole lot of sense, but when you are dealing with the extremely low levels of power used by LEDs, a lot of things don't make sense. A single 6W bulb uses only 50 milliamps!
As noted in the installation manual:

CFLs or LEDs do not dim, have a poor dimming range, or they flicker / flash.
Verify Step 7. Ensure bulbs are Lutron compatible.

and

Audible buzzing (common with LEDs).
If bothersome, use a different bulb.

Lutron has a complete list online.
I recommend getting bulbs on the official list. There is a good chance that a newer bulb from a manufacturer on the list will also work. But the &quot;unknowns&quot; - hit and miss - and in this case &quot;miss&quot;.
The alternative is to get a dimmer that requires either ground or neutral, provided your switch location has the necessary ground or neutral wire. Those will definitely avoid any &quot;blink when off&quot; problems, but might still have blink when on problems if used with a non-dimmer-compatible or, as seems to be your case, non-quite-compatible-enough bulb.