Continuity

Spoilers for Rogue One below the fold

It is a period of civil war. Rebel spaceships, striking from a hidden base, have won their first victory against the evil Galactic Empire. During the battle, Rebel spies managed to steal secret plans to the Empire's ultimate weapon, the DEATH STAR, an armored space station with enough power to destroy an entire planet.

―Episode IV opening crawl

Rogue One ends with the Battle of Scarif. During this battle, many things are going on at once, as is typical for a Star Wars battle.

• On the surface, team Rogue One steals the tape holding the plans from the archive tower, then climbs the tower to the high-gain antenna on top. No high-bandwidth signals can get through the shield, and the plans are sufficiently large that a high-bandwidth signal is needed.
• Simultaneously their ship is patched into the base comm system. A low-bandwidth (voice) signal is sent up telling the fleet to be ready for a large transmission, and to take the shield down in order to get it. The fleet knows what Rogue One is looking for in general, because they talked about it in council before Rogue One went rogue.
• The fleet takes down the shield by destroying the shield gate. Apparently the shield was generated from there.
• Once the shield is down and the antennas are aligned, the data is transmitted to the rebel fleet flagship Profundity and copied onto a physical storage medium ("tape").
• The Death Star arrives but ignores the fleet. They know that Vader is arriving soon to deal with the fleet, and they don't know who to point the big gun at. For all they know, there might be a copy of the plans in every ship in the fleet. In fact, only Profundity has a copy.
• Vader arrives in Devastator exactly as the fleet is attempting to jump to hyperspace and escape. Several ships, including Profundity, are intercepted.
• The tape is hand-carried to the docking bay of Profundity where it is slipped through the airlock door of Tantive IV just as it is launching. Vader personally tried but failed to stop this hand-off. Tantive IV escapes into hyperspace.

So at this point, Vader knows that several ships escaped before he got there, but probably from interrogating the crew of Profundity, they knew that it was on that blockade runner that escaped, and probably the registration of it, so they knew they were looking for Tantive IV, but might not have known who was on it.

An unknown amount of time later, Devastator intercepts Tantive IV over Tatooine. (It is possible that Tantive IV took an indirect route from Scarif to Tatooine. I don't know if it matters.) Tantive IV is looking for General Kenobi, and somehow Devastator tracked them there. Presumably Tantive IV arrived first and was following normal protocols for landing in the wilderness when Devastator showed up. Kenobi didn't know at that time that anyone was coming.

               INT. REBEL BLOCKADE RUNNER - CORRIDOR

               The evil Darth Vader stands amid the broken and twisted bodies 
               of his foes. He grabs a wounded Rebel Officer by the neck as 
               an Imperial Officer rushes up to the Dark Lord.

                                     IMPERIAL OFFICER
                         The Death Star plans are not in the 
                         main computer.

               Vader squeezes the neck of the Rebel Officer, who struggles 
               in vain.

                                     VADER
                         Where are those transmissions you 
                         intercepted?

               Vader lifts the Rebel off his feet by his throat.

                                     VADER
                         What have you done with those plans?

                                     REBEL OFFICER
                         We intercepted no transmissions. 
                         Aaah... This is a consular ship. 
                         Were on a diplomatic mission.

                                     VADER
                         If this is a consular ship... were 
                         is the Ambassador?

               The Rebel refuses to speak but eventually cries out as the 
               Dark Lord begins to squeeze the officer's throat, creating a 
               gruesome snapping and choking, until the soldier goes limp. 
               Vader tosses the dead soldier against the wall and turns to 
               his troops.

                                     VADER
                         Commander, tear this ship apart until 
                         you've found those plans and bring 
                         me the Ambassador. I want her alive!

               The stormtroopers scurry into the subhallways.

The "transmission" was a transmission (from Rogue One to Profundity) but is a physical tape at this point. Vader knows that Tantive IV was at Scarif and was the ship that escaped with the tapes, but no one on Tantive IV knows that the star destroyer that intercepted Profundity was Vader's ship, so the captain tried to bluff his way out.