Ambient backscatter communications (AmBC), where a backscatter transmitter (BT) modulates and reflects ambient signals to a backscatter receiver (BR), have been deemed a low-power communication technology for the Internet of Things. Previous work on symbol detection in AmBC assumed perfect time synchronization (TS), which is unrealistic in practice. The residual TS errors (RTSE) cause \emph{partial sample mismatch}, degrading symbol detection performance. To address this, we propose a new AmBC symbol detection framework that incorporates the BT's current and adjacent symbols, as well as channel coefficients. Using energy detector (ED) as a case study, we derive both exact and approximate bit error rate (BER) expressions. Our results show that the ED's BER performance degrades significantly under RTSE, with the symbol detection threshold optimized under the assumption of perfect TS. We then derive a closed-form expression for a near-optimal symbol detection threshold that minimizes BER under RTSE. To estimate the required parameters for the detection threshold, we propose a novel method exploiting the attributes of the BR's received signal samples. The analytical results are verified by simulation results.