A CPR HAWKER 800 HAD LTSS WITH AN ACR JETSTREAM. HAWKER ERROR ADMITTED.

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WE DEPARTED SNA IFR FOR LAS. WE WERE ON THE MUSEL 5 DEP; THERMAL TRANSITION. WE WERE ON VECTORS FOR TFC. NEAR MUSEL INTXN; THE CTLR CALLED OUT TFC AT OUR 10 O'CLOCK; 5 MI AND COPLT RESPONDED THAT WE HAD TFC IN SIGHT. I LOOKED TO SEE WHERE TFC WAS AND INADVERTENTLY PULLED BACK ON THE YOKE. WHEN I LOOKED BACK AT THE PANEL; WE WERE 250 FT HIGH FROM THE ASSIGNED ALT OF 6000 FT. I STARTED BACK DOWN TO THE PROPER ALT. THE CTLR CALLED AND SAID SHE HAD US HIGH FROM ASSIGNED ALT. SHE ASKED THE JETSTREAM IF WE WERE IN SIGHT AND HE SAID YES. SHE THEN SAID FOR THE JETSTREAM TO MAINTAIN VISUAL CONTACT. THE CTLR THEN TOLD US TO TURN L TO A SE HEADING AND INTERCEPT THE DEP. AFTER A COUPLE OF MINS; SHE CALLED AND SAID THAT SHE NEEDED US TO CALL THE FACILITY WHEN WE GOT ON THE GND. WE DID. SHE SAID WE CAUSED A PLTDEV. SHE SAID SHE NEEDED 1000 FT VERT SEPARATION OR 3 MI HORIZ SEPARATION OR VISUAL CONTACT. THE JETSTREAM HAD TO TURN L A FEW DEGS AS DIRECTED BY THE CTLR. WE HAD THE JETSTREAM IN SIGHT AND IT WAS NO FACTOR. SUPPLEMENTAL INFO FROM ACN 341663: THE CTLR STATED WE WERE 500 FT OFF OUR ALT AND LOST SEPARATION BTWN OUR 2 ACFT. I NEVER WITNESSED A DEV ANY LARGER THAN 250 FT NOR DID OUR ALT ALERTER ALARMS EVER ACTIVATE; INDICATING THE DEV WAS KEPT TO A MINIMUM.