DROP TABLE IF EXISTS wages,tips;
CREATE TABLE wages( id int, waiter int, start date, rate decimal(6,2));
INSERT INTO wages VALUES
( 1, 4, '2025-01-01', 5.00 ),
( 2, 4, '2025-03-01', 6.00 ),
( 3, 5, '2025-01-05', 7.00 ),
( 4, 5, '2024-03-20', 8.00 ),
( 5, 5, '2024-04-01', 9.00 );
CREATE TABLE tips(
  id int, 
  date date, 
  waiter int, 
  hours_worked smallint, 
  tabs smallint, 
  tips decimal(6,2)
);
INSERT INTO tips VALUES
( 1, '2025-02-29', 4, 6.50, 21, 65.25 ),
( 2, '2025-03-06', 5, 6.00, 15, 51.75 ),
( 3, '2024-03-21', 4, 2.50, 5, 17.85 ),
( 4, '2024-03-22', 5, 5.25, 10, 39.00 );
SELECT * FROM wages;
+------+--------+------------+------+
| id   | waiter | start      | rate |
+------+--------+------------+------+
|    1 |      4 | 2025-01-01 | 5.00 |
|    2 |      4 | 2025-03-01 | 6.00 |
|    3 |      5 | 2025-01-05 | 7.00 |
|    4 |      5 | 2024-03-20 | 8.00 |
|    5 |      5 | 2024-04-01 | 9.00 |
+------+--------+------------+------+
SELECT * FROM tips;
+------+------------+--------+--------------+------+-------+
| id   | date       | waiter | hours_worked | tabs | tips  |
+------+------------+--------+--------------+------+-------+
|    1 | 2025-02-29 |      4 |            7 |   21 | 65.25 |
|    2 | 2025-03-06 |      5 |            6 |   15 | 51.75 |
|    3 | 2024-03-21 |      4 |            3 |    5 | 17.85 |
|    4 | 2024-03-22 |      5 |            5 |   10 | 39.00 |
+------+------------+--------+--------------+------+-------+

+------+------------+------+------+-------+------+--------+------+------------+
| tid  | Date       | Hrs  | tabs | tips  | wid  | waiter | rate | start      |
+------+------------+------+------+-------+------+--------+------+------------+
|    1 | 2025-02-29 |    7 |   21 | 65.25 |    2 |      4 | 6.00 | 2025-03-01 |
|    2 | 2025-03-06 |    6 |   15 | 51.75 |    3 |      5 | 7.00 | 2025-01-05 |
|    3 | 2024-03-21 |    3 |    5 | 17.85 |    2 |      4 | 6.00 | 2025-03-01 |
|    4 | 2024-03-22 |    5 |   10 | 39.00 |    4 |      5 | 8.00 | 2024-03-20 |
+------+------------+------+------+-------+------+--------+------+------------+

One way to proceed is to build a temporary table from a join of wages to tips on waiter and wages.start < tips.date, then exclusion-join that result to itself to remove all rows except those with the latest wage rate per tips row. A two-step:

-- wages-tips join removing later wage changes:
DROP TABLE IF EXISTS tmp;
CREATE TABLE tmp
SELECT 
  t.id AS tid, t.date AS Date, t.hours_worked AS Hrs,t.tabs,t.tips,
  w.id AS wid, w.waiter, w.rate, w.start
FROM tips t
JOIN wages w ON w.waiter=t.waiter AND w.start<=t.date;
-- self-exclusion join to remove obsolete wage rows:
SELECT t1.*
FROM tmp t1
LEFT JOIN tmp t2 ON t1.tid=t2.tid and t1.start
As of MySQL 8 and MariaDB 10.2, the intermediary table code can be a Common Table Expression:
WITH tmp AS (
  SELECT 
    t.id AS tid, t.date AS Date, t.hours_worked AS Hrs,t.tabs,t.tips,
    w.id AS wid, w.waiter, w.rate, w.start
  FROM tips t
  JOIN wages w ON w.waiter=t.waiter AND w.start<=t.date
)
SELECT t1.*
FROM tmp t1
LEFT JOIN tmp t2 ON t1.tid=t2.tid and t1.start
Can we skip the temp table, event the virtual one? Yes—by adding the condition wages.start <= tips.date to each side of the exclusion join:
SELECT 
  t.id AS tid, t.date, t.hours_worked AS Hrs,t.tabs,t.tips,
  w.id AS wid, w.waiter, w.rate, w.start
FROM tips t
JOIN wages w ON w.waiter=t.waiter AND w.start <= t.date
LEFT JOIN wages w2 ON w.waiter=w2.waiter AND w2.start<=t.date AND w.start
Simpler, gives the same result as the CTE, and slightly faster.