We do not learn a whole lot about Juliet's feelings for Tybalt, so we do not really know how Tybalt's death truly affects her, accept in the way that his death is associated with Romeo.
We can assume from Act 3, Scene 2 that Juliet cared very much about her cousin and that the news of his death shocked her. When Juliet is still trying to find out from her Nurse exactly what happened to Tybalt and Romeo, she refers to Tybalt as "my dear-loved cousin," and to Romeo as "my dearer lord." The phrase referring to Tybalt tells us that Juliet did truly care for Tybalt and is distressed to hear he has been killed. Her love for Tybalt can also help to explain why Juliet felt so deceived by Romeo when she first learns that Romeo killed Tybalt. It is not just the fact that Romeo committed a murder that makes her next call him a "fiend angelical!," it is the fact that Romeo killed someone she loves that is making her feel so beguiled. Juliet's string of oxymorons show us just how duped she feels by Romeo and his charms:
Beautiful tyrant! fiend angelical!
Dove-feather'd raven! wolvish-ravening lamb
Just opposite to what thou justly seem'st,
A damned saint, an honourable villain! (III.ii)
However, her love for Romeo soon outweighs her love for Tybalt and, soon realizing that Tybalt would have killed Romeo had he not killed Tybalt first, she forgives Romeo and quickly restores her faith in him. The sorrow she felt over Tybalt's death is soon drowned by the realization that Romeo has been banished.
Similarly, her love for Romeo makes her feel anguished when she awakes in the tomb in the final scene realizing that Romeo has poisoned himself to death. Now that her husband is dead, she does not feel that she can continue living and first tries to poison herself by kissing his lips and then kills herself with his dagger.
Hence, Juliet is sorrowful and feels deceived by Romeo when she first learns that Tybalt has been killed, but her love for Romeo makes her quickly feel differently. In the end, Juliet feels agony over Romeo's death.